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[Title]
䐔(4܂ŋ߂)

% 蕶
% Ȃ΁C[Level1]ɏ̂̂܂ܖ蕶ƂȂB
[Problem]
̈ʍ͏AƂȂ铙䐔$\{a_n\}$ɂāA4܂ł߂B

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[FontSize]
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[usepackage]
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% ꂼ̖𓚂$\displaystyle $tȂꍇ́COFF܂0
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[displaystyle]
OFF


% Level1̖BȉLevel7܂œlB
% 1sڂɂ͏ڍאݒ̃^CgB
% 2sڈȍ~ɖƂ̉𓚂B
% Ɖ𓚁C𓚂Ɩ͂PsďB
% vZߒꍇ́CƉ𓚂̊ԂɂPsԊuC
% ŏprocessƂsC̎̍svZߒĂB
[Level1]
ʍ()

$a_n= (-3)^{n}$

$-3, 9, -27, 81$

$a_n=-3  (-2)^{n-1}$

$-3, 6, -12, 24$

$a_n=-3  (-1)^{n-1}$

$-3, 3, -3, 3$

$a_n=-3 \cdot 2^{n-1}$

$-3, -6, -12, -24$

$a_n=- 3^{n}$

$-3, -9, -27, -81$

$a_n=-2  (-3)^{n-1}$

$-2, 6, -18, 54$

$a_n= (-2)^{n}$

$-2, 4, -8, 16$

$a_n=-2  (-1)^{n-1}$

$-2, 2, -2, 2$

$a_n=- 2^{n}$

$-2, -4, -8, -16$

$a_n=-2 \cdot 3^{n-1}$

$-2, -6, -18, -54$

$a_n= -(-3)^{n-1}$

$-1, 3, -9, 27$

$a_n= -(-2)^{n-1}$

$-1, 2, -4, 8$

$a_n= (-1)^{n}$

$-1, 1, -1, 1$

$a_n= -2^{n-1}$

$-1, -2, -4, -8$

$a_n= -3^{n-1}$

$-1, -3, -9, -27$

$a_n= (-3)^{n-1}$

$1, -3, 9, -27$

$a_n= (-2)^{n-1}$

$1, -2, 4, -8$

$a_n= (-1)^{n-1}$

$1, -1, 1, -1$

$a_n= 2^{n-1}$

$1, 2, 4, 8$

$a_n= 3^{n-1}$

$1, 3, 9, 27$

$a_n=2  (-3)^{n-1}$

$2, -6, 18, -54$

$a_n=- (-2)^{n}$

$2, -4, 8, -16$

$a_n=2  (-1)^{n-1}$

$2, -2, 2, -2$

$a_n= 2^{n}$

$2, 4, 8, 16$

$a_n=2 \cdot 3^{n-1}$

$2, 6, 18, 54$

$a_n=- (-3)^{n}$

$3, -9, 27, -81$

$a_n=3  (-2)^{n-1}$

$3, -6, 12, -24$

$a_n=3  (-1)^{n-1}$

$3, -3, 3, -3$

$a_n=3 \cdot 2^{n-1}$

$3, 6, 12, 24$

$a_n= 3^{n}$

$3, 9, 27, 81$




[Level2]
ʍ()

$a_n=-3 \left( \nfrac12 \right)^{n-1}$

$-3, -\nfrac32, -\nfrac34, -\nfrac38$

$a_n=-3 \left(- \nfrac12 \right)^{n-1}$

$-3, \nfrac32, -\nfrac34, \nfrac38$

$a_n=-3 \left( \nfrac13 \right)^{n-1}$

$-3, -1, -\nfrac13, -\nfrac19$

$a_n=-3 \left(- \nfrac13 \right)^{n-1}$

$-3, 1, -\nfrac13, \nfrac19$

$a_n=-2 \left( \nfrac12 \right)^{n-1}$

$-2, -1, -\nfrac12, -\nfrac14$

$a_n=-2 \left(- \nfrac12 \right)^{n-1}$

$-2, 1, -\nfrac12, \nfrac14$

$a_n=-2 \left( \nfrac13 \right)^{n-1}$

$-2, -\nfrac23, -\nfrac29, -\nfrac{2}{27}$

$a_n=-2 \left(- \nfrac13 \right)^{n-1}$

$-2, \nfrac23, -\nfrac29, \nfrac{2}{27}$

$a_n= -\left( \nfrac12 \right)^{n-1}$

$-1, -\nfrac12, -\nfrac14, -\nfrac18$

$a_n= -\left(- \nfrac12 \right)^{n-1}$

$-1, \nfrac12, -\nfrac14, \nfrac18$

$a_n= -\left( \nfrac13 \right)^{n-1}$

$-1, -\nfrac13, -\nfrac19, -\nfrac{1}{27}$

$a_n= -\left(- \nfrac13 \right)^{n-1}$

$-1, \nfrac13, -\nfrac19, \nfrac{1}{27}$

$a_n= \left( \nfrac12 \right)^{n-1}$

$1, \nfrac12, \nfrac14, \nfrac18$

$a_n= \left(- \nfrac12 \right)^{n-1}$

$1, -\nfrac12, \nfrac14, -\nfrac18$

$a_n= \left( \nfrac13 \right)^{n-1}$

$1, \nfrac13, \nfrac19, \nfrac{1}{27}$

$a_n= \left(- \nfrac13 \right)^{n-1}$

$1, -\nfrac13, \nfrac19, -\nfrac{1}{27}$

$a_n=2 \left( \nfrac12 \right)^{n-1}$

$2, 1, \nfrac12, \nfrac14$

$a_n=2 \left(- \nfrac12 \right)^{n-1}$

$2, -1, \nfrac12, -\nfrac14$

$a_n=2 \left( \nfrac13 \right)^{n-1}$

$2, \nfrac23, \nfrac29, \nfrac{2}{27}$

$a_n=2 \left(- \nfrac13 \right)^{n-1}$

$2, -\nfrac23, \nfrac29, -\nfrac{2}{27}$

$a_n=3 \left( \nfrac12 \right)^{n-1}$

$3, \nfrac32, \nfrac34, \nfrac38$

$a_n=3 \left(- \nfrac12 \right)^{n-1}$

$3, -\nfrac32, \nfrac34, -\nfrac38$

$a_n=3 \left( \nfrac13 \right)^{n-1}$

$3, 1, \nfrac13, \nfrac19$

$a_n=3 \left(- \nfrac13 \right)^{n-1}$

$3, -1, \nfrac13, -\nfrac19$

$a_n=\nfrac12  (-3)^{n-1}$

$\nfrac12, -\nfrac32, \nfrac92, -\nfrac{27}{2}$

$a_n=\nfrac12  (-2)^{n-1}$

$\nfrac12, -1, 2, -4$

$a_n=\nfrac12  (-1)^{n-1}$

$\nfrac12, -\nfrac12, \nfrac12, -\nfrac12$

$a_n=\nfrac12 \cdot 2^{n-1}$

$\nfrac12, 1, 2, 4$

$a_n=\nfrac12 \cdot 3^{n-1}$

$\nfrac12, \nfrac32, \nfrac92, \nfrac{27}{2}$

$a_n= \left( \nfrac12 \right)^{n}$

$\nfrac12, \nfrac14, \nfrac18, \nfrac{1}{16}$

$a_n=- \left(- \nfrac12 \right)^{n}$

$\nfrac12, -\nfrac14, \nfrac18, -\nfrac{1}{16}$

$a_n=\nfrac12 \left( \nfrac13 \right)^{n-1}$

$\nfrac12, \nfrac16, \nfrac{1}{18}, \nfrac{1}{54}$

$a_n=\nfrac12 \left(- \nfrac13 \right)^{n-1}$

$\nfrac12, -\nfrac16, \nfrac{1}{18}, -\nfrac{1}{54}$

$a_n=-\nfrac12  (-3)^{n-1}$

$-\nfrac12, \nfrac32, -\nfrac92, \nfrac{27}{2}$

$a_n=-\nfrac12  (-2)^{n-1}$

$-\nfrac12, 1, -2, 4$

$a_n=-\nfrac12  (-1)^{n-1}$

$-\nfrac12, \nfrac12, -\nfrac12, \nfrac12$

$a_n=-\nfrac12 \cdot 2^{n-1}$

$-\nfrac12, -1, -2, -4$

$a_n=-\nfrac12 \cdot 3^{n-1}$

$-\nfrac12, -\nfrac32, -\nfrac92, -\nfrac{27}{2}$

$a_n=- \left( \nfrac12 \right)^{n}$

$-\nfrac12, -\nfrac14, -\nfrac18, -\nfrac{1}{16}$

$a_n= \left(- \nfrac12 \right)^{n}$

$-\nfrac12, \nfrac14, -\nfrac18, \nfrac{1}{16}$

$a_n=-\nfrac12 \left( \nfrac13 \right)^{n-1}$

$-\nfrac12, -\nfrac16, -\nfrac{1}{18}, -\nfrac{1}{54}$

$a_n=-\nfrac12 \left(- \nfrac13 \right)^{n-1}$

$-\nfrac12, \nfrac16, -\nfrac{1}{18}, \nfrac{1}{54}$

$a_n=\nfrac13  (-3)^{n-1}$

$\nfrac13, -1, 3, -9$

$a_n=\nfrac13  (-2)^{n-1}$

$\nfrac13, -\nfrac23, \nfrac43, -\nfrac83$

$a_n=\nfrac13  (-1)^{n-1}$

$\nfrac13, -\nfrac13, \nfrac13, -\nfrac13$

$a_n=\nfrac13 \cdot 2^{n-1}$

$\nfrac13, \nfrac23, \nfrac43, \nfrac83$

$a_n=\nfrac13 \cdot 3^{n-1}$

$\nfrac13, 1, 3, 9$

$a_n=\nfrac13 \left( \nfrac12 \right)^{n-1}$

$\nfrac13, \nfrac16, \nfrac{1}{12}, \nfrac{1}{24}$

$a_n=\nfrac13 \left(- \nfrac12 \right)^{n-1}$

$\nfrac13, -\nfrac16, \nfrac{1}{12}, -\nfrac{1}{24}$

$a_n= \left( \nfrac13 \right)^{n}$

$\nfrac13, \nfrac19, \nfrac{1}{27}, \nfrac{1}{81}$

$a_n=- \left(- \nfrac13 \right)^{n}$

$\nfrac13, -\nfrac19, \nfrac{1}{27}, -\nfrac{1}{81}$

$a_n=-\nfrac13 (-3)^{n-1}$

$-\nfrac13, 1, -3, 9$

$a_n=-\nfrac13 (-2)^{n-1}$

$-\nfrac13, \nfrac23, -\nfrac43, \nfrac83$

$a_n=-\nfrac13 (-1)^{n-1}$

$-\nfrac13, \nfrac13, -\nfrac13, \nfrac13$

$a_n=-\nfrac13 \cdot 2^{n-1}$

$-\nfrac13, -\nfrac23, -\nfrac43, -\nfrac83$

$a_n=-\nfrac13 \cdot 3^{n-1}$

$-\nfrac13, -1, -3, -9$

$a_n=-\nfrac13 \left( \nfrac12 \right)^{n-1}$

$-\nfrac13, -\nfrac16, -\nfrac{1}{12}, -\nfrac{1}{24}$

$a_n=-\nfrac13 \left(- \nfrac12 \right)^{n-1}$

$-\nfrac13, \nfrac16, -\nfrac{1}{12}, \nfrac{1}{24}$

$a_n=- \left( \nfrac13 \right)^{n}$

$-\nfrac13, -\nfrac19, -\nfrac{1}{27}, -\nfrac{1}{81}$

$a_n= \left(- \nfrac13 \right)^{n}$

$-\nfrac13, \nfrac19, -\nfrac{1}{27}, \nfrac{1}{81}$




[Level3]
ʍ([g)

$a_n=\sqrt2  (-3)^{n-1}$

$\sqrt2, -3\sqrt2, 9\sqrt2, -27\sqrt2$

$a_n=\sqrt2  (-2)^{n-1}$

$\sqrt2, -2\sqrt2, 4\sqrt2, -8\sqrt2$

$a_n=\sqrt2  (-1)^{n-1}$

$\sqrt2, -\sqrt2, \sqrt2, -\sqrt2$

$a_n=\sqrt2 \cdot 2^{n-1}$

$\sqrt2, 2\sqrt2, 4\sqrt2, 8\sqrt2$

$a_n=\sqrt2 \cdot 3^{n-1}$

$\sqrt2, 3\sqrt2, 9\sqrt2, 27\sqrt2$

$a_n= \left( \sqrt2 \right)^{n}$

$\sqrt2, 2, 2\sqrt2, 4$

$a_n=- \left( -\sqrt2 \right)^{n}$

$\sqrt2, -2, 2\sqrt2, -4$

$a_n=\sqrt2 \left( \sqrt3 \right)^{n-1}$

$\sqrt2, \sqrt6, 3\sqrt2, 3\sqrt6$

$a_n=\sqrt2 \left( -\sqrt3 \right)^{n-1}$

$\sqrt2, -\sqrt6, 3\sqrt2, -3\sqrt6$

$a_n=-\sqrt2  (-3)^{n-1}$

$-\sqrt2, 3\sqrt2, -9\sqrt2, 27\sqrt2$

$a_n=-\sqrt2  (-2)^{n-1}$

$-\sqrt2, 2\sqrt2, -4\sqrt2, 8\sqrt2$

$a_n=-\sqrt2  (-1)^{n-1}$

$-\sqrt2, \sqrt2, -\sqrt2, \sqrt2$

$a_n=-\sqrt2 \cdot 2^{n-1}$

$-\sqrt2, -2\sqrt2, -4\sqrt2, -8\sqrt2$

$a_n=-\sqrt2 \cdot 3^{n-1}$

$-\sqrt2, -3\sqrt2, -9\sqrt2, -27\sqrt2$

$a_n=- \left( \sqrt2 \right)^{n}$

$-\sqrt2, -2, -2\sqrt2, -4$

$a_n= \left( -\sqrt2 \right)^{n}$

$-\sqrt2, 2, -2\sqrt2, 4$

$a_n=-\sqrt2 \left( \sqrt3 \right)^{n-1}$

$-\sqrt2, -\sqrt6, -3\sqrt2, -3\sqrt6$

$a_n=-\sqrt2 \left( -\sqrt3 \right)^{n-1}$

$-\sqrt2, \sqrt6, -3\sqrt2, 3\sqrt6$

$a_n=\sqrt3  (-3)^{n-1}$

$\sqrt3, -3\sqrt3, 9\sqrt3, -27\sqrt3$

$a_n=\sqrt3  (-2)^{n-1}$

$\sqrt3, -2\sqrt3, 4\sqrt3, -8\sqrt3$

$a_n=\sqrt3  (-1)^{n-1}$

$\sqrt3, -\sqrt3, \sqrt3, -\sqrt3$

$a_n=\sqrt3 \cdot 2^{n-1}$

$\sqrt3, 2\sqrt3, 4\sqrt3, 8\sqrt3$

$a_n=\sqrt3 \cdot 3^{n-1}$

$\sqrt3, 3\sqrt3, 9\sqrt3, 27\sqrt3$

$a_n=\sqrt3 \left( \sqrt2 \right)^{n-1}$

$\sqrt3, \sqrt6, 2\sqrt3, 2\sqrt6$

$a_n=\sqrt3 \left( -\sqrt2 \right)^{n-1}$

$\sqrt3, -\sqrt6, 2\sqrt3, -2\sqrt6$

$a_n= \left( \sqrt3 \right)^{n}$

$\sqrt3, 3, 3\sqrt3, 9$

$a_n=- \left( -\sqrt3 \right)^{n}$

$\sqrt3, -3, 3\sqrt3, -9$

$a_n=-\sqrt3  (-3)^{n-1}$

$-\sqrt3, 3\sqrt3, -9\sqrt3, 27\sqrt3$

$a_n=-\sqrt3  (-2)^{n-1}$

$-\sqrt3, 2\sqrt3, -4\sqrt3, 8\sqrt3$

$a_n=-\sqrt3  (-1)^{n-1}$

$-\sqrt3, \sqrt3, -\sqrt3, \sqrt3$

$a_n=-\sqrt3 \cdot 2^{n-1}$

$-\sqrt3, -2\sqrt3, -4\sqrt3, -8\sqrt3$

$a_n=-\sqrt3 \cdot 3^{n-1}$

$-\sqrt3, -3\sqrt3, -9\sqrt3, -27\sqrt3$

$a_n=-\sqrt3 \left( \sqrt2 \right)^{n-1}$

$-\sqrt3, -\sqrt6, -2\sqrt3, -2\sqrt6$

$a_n=-\sqrt3 \left( -\sqrt2 \right)^{n-1}$

$-\sqrt3, \sqrt6, -2\sqrt3, 2\sqrt6$

$a_n=- \left( \sqrt3 \right)^{n}$

$-\sqrt3, -3, -3\sqrt3, -9$

$a_n= \left( -\sqrt3 \right)^{n}$

$-\sqrt3, 3, -3\sqrt3, 9$

$a_n=-3 \left( \sqrt2 \right)^{n-1}$

$-3, -3\sqrt2, -6, -6\sqrt2$

$a_n=-3 \left( -\sqrt2 \right)^{n-1}$

$-3, 3\sqrt2, -6, 6\sqrt2$

$a_n=-3 \left( \sqrt3 \right)^{n-1}$

$-3, -3\sqrt3, -9, -9\sqrt3$

$a_n=-3 \left( -\sqrt3 \right)^{n-1}$

$-3, 3\sqrt3, -9, 9\sqrt3$

$a_n=-2 \left( \sqrt2 \right)^{n-1}$

$-2, -2\sqrt2, -4, -4\sqrt2$

$a_n=-2 \left( -\sqrt2 \right)^{n-1}$

$-2, 2\sqrt2, -4, 4\sqrt2$

$a_n=-2 \left( \sqrt3 \right)^{n-1}$

$-2, -2\sqrt3, -6, -6\sqrt3$

$a_n=-2 \left( -\sqrt3 \right)^{n-1}$

$-2, 2\sqrt3, -6, 6\sqrt3$

$a_n= -\left( \sqrt2 \right)^{n-1}$

$-1, -\sqrt2, -2, -2\sqrt2$

$a_n= -\left( -\sqrt2 \right)^{n-1}$

$-1, \sqrt2, -2, 2\sqrt2$

$a_n= -\left( \sqrt3 \right)^{n-1}$

$-1, -\sqrt3, -3, -3\sqrt3$

$a_n= -\left( -\sqrt3 \right)^{n-1}$

$-1, \sqrt3, -3, 3\sqrt3$

$a_n= \left( \sqrt2 \right)^{n-1}$

$1, \sqrt2, 2, 2\sqrt2$

$a_n= \left( -\sqrt2 \right)^{n-1}$

$1, -\sqrt2, 2, -2\sqrt2$

$a_n= \left( \sqrt3 \right)^{n-1}$

$1, \sqrt3, 3, 3\sqrt3$

$a_n= \left( -\sqrt3 \right)^{n-1}$

$1, -\sqrt3, 3, -3\sqrt3$

$a_n=2 \left( \sqrt2 \right)^{n-1}$

$2, 2\sqrt2, 4, 4\sqrt2$

$a_n=2 \left( -\sqrt2 \right)^{n-1}$

$2, -2\sqrt2, 4, -4\sqrt2$

$a_n=2 \left( \sqrt3 \right)^{n-1}$

$2, 2\sqrt3, 6, 6\sqrt3$

$a_n=2 \left( -\sqrt3 \right)^{n-1}$

$2, -2\sqrt3, 6, -6\sqrt3$

$a_n=3 \left( \sqrt2 \right)^{n-1}$

$3, 3\sqrt2, 6, 6\sqrt2$

$a_n=3 \left( -\sqrt2 \right)^{n-1}$

$3, -3\sqrt2, 6, -6\sqrt2$

$a_n=3 \left( \sqrt3 \right)^{n-1}$

$3, 3\sqrt3, 9, 9\sqrt3$

$a_n=3 \left( -\sqrt3 \right)^{n-1}$

$3, -3\sqrt3, 9, -9\sqrt3$




[Level4]
ʍ([g)

$a_n=\nfrac12 \left( \sqrt2 \right)^{n-1}$

$\nfrac12, \nfrac{\sqrt2}{2}, 1, \sqrt2$

$a_n=\nfrac12 \left( -\sqrt2 \right)^{n-1}$

$\nfrac12, -\nfrac{\sqrt2}{2}, 1, -\sqrt2$

$a_n=\nfrac12 \left( \sqrt3 \right)^{n-1}$

$\nfrac12, \nfrac{\sqrt3}{2}, \nfrac32, \nfrac{3\sqrt3}{2}$

$a_n=\nfrac12 \left( -\sqrt3 \right)^{n-1}$

$\nfrac12, -\nfrac{\sqrt3}{2}, \nfrac32, -\nfrac{3\sqrt3}{2}$

$a_n=-\nfrac12 \left( \sqrt2 \right)^{n-1}$

$-\nfrac12, -\nfrac{\sqrt2}{2}, -1, -\sqrt2$

$a_n=-\nfrac12 \left( -\sqrt2 \right)^{n-1}$

$-\nfrac12, \nfrac{\sqrt2}{2}, -1, \sqrt2$

$a_n=-\nfrac12 \left( \sqrt3 \right)^{n-1}$

$-\nfrac12, -\nfrac{\sqrt3}{2}, -\nfrac32, -\nfrac{3\sqrt3}{2}$

$a_n=-\nfrac12 \left( -\sqrt3 \right)^{n-1}$

$-\nfrac12, \nfrac{\sqrt3}{2}, -\nfrac32, \nfrac{3\sqrt3}{2}$

$a_n=\nfrac13 \left( \sqrt2 \right)^{n-1}$

$\nfrac13, \nfrac{\sqrt2}{3}, \nfrac23, \nfrac{2\sqrt2}{3}$

$a_n=\nfrac13 \left( -\sqrt2 \right)^{n-1}$

$\nfrac13, -\nfrac{\sqrt2}{3}, \nfrac23, -\nfrac{2\sqrt2}{3}$

$a_n=\nfrac13 \left( \sqrt3 \right)^{n-1}$

$\nfrac13, \nfrac{\sqrt3}{3}, 1, \sqrt3$

$a_n=\nfrac13 \left( -\sqrt3 \right)^{n-1}$

$\nfrac13, -\nfrac{\sqrt3}{3}, 1, -\sqrt3$

$a_n=-\nfrac13 \left( \sqrt2 \right)^{n-1}$

$-\nfrac13, -\nfrac{\sqrt2}{3}, -\nfrac23, -\nfrac{2\sqrt2}{3}$

$a_n=-\nfrac13 \left( -\sqrt2 \right)^{n-1}$

$-\nfrac13, \nfrac{\sqrt2}{3}, -\nfrac23, \nfrac{2\sqrt2}{3}$

$a_n=-\nfrac13 \left( \sqrt3 \right)^{n-1}$

$-\nfrac13, -\nfrac{\sqrt3}{3}, -1, -\sqrt3$

$a_n=-\nfrac13 \left( -\sqrt3 \right)^{n-1}$

$-\nfrac13, \nfrac{\sqrt3}{3}, -1, \sqrt3$

$a_n=\sqrt2 \left( \nfrac12 \right)^{n-1}$

$\sqrt2, \nfrac{\sqrt2}{2}, \nfrac{\sqrt2}{4}, \nfrac{\sqrt2}{8}$

$a_n=\sqrt2 \left(- \nfrac12 \right)^{n-1}$

$\sqrt2, -\nfrac{\sqrt2}{2}, \nfrac{\sqrt2}{4}, -\nfrac{\sqrt2}{8}$

$a_n=\sqrt2 \left( \nfrac13 \right)^{n-1}$

$\sqrt2, \nfrac{\sqrt2}{3}, \nfrac{\sqrt2}{9}, \nfrac{\sqrt2}{27}$

$a_n=\sqrt2 \left(- \nfrac13 \right)^{n-1}$

$\sqrt2, -\nfrac{\sqrt2}{3}, \nfrac{\sqrt2}{9}, -\nfrac{\sqrt2}{27}$

$a_n=-\sqrt2 \left( \nfrac12 \right)^{n-1}$

$-\sqrt2, -\nfrac{\sqrt2}{2}, -\nfrac{\sqrt2}{4}, -\nfrac{\sqrt2}{8}$

$a_n=-\sqrt2 \left(- \nfrac12 \right)^{n-1}$

$-\sqrt2, \nfrac{\sqrt2}{2}, -\nfrac{\sqrt2}{4}, \nfrac{\sqrt2}{8}$

$a_n=-\sqrt2 \left( \nfrac13 \right)^{n-1}$

$-\sqrt2, -\nfrac{\sqrt2}{3}, -\nfrac{\sqrt2}{9}, -\nfrac{\sqrt2}{27}$

$a_n=-\sqrt2 \left(- \nfrac13 \right)^{n-1}$

$-\sqrt2, \nfrac{\sqrt2}{3}, -\nfrac{\sqrt2}{9}, \nfrac{\sqrt2}{27}$

$a_n=\sqrt3 \left( \nfrac12 \right)^{n-1}$

$\sqrt3, \nfrac{\sqrt3}{2}, \nfrac{\sqrt3}{4}, \nfrac{\sqrt3}{8}$

$a_n=\sqrt3 \left(- \nfrac12 \right)^{n-1}$

$\sqrt3, -\nfrac{\sqrt3}{2}, \nfrac{\sqrt3}{4}, -\nfrac{\sqrt3}{8}$

$a_n=\sqrt3 \left( \nfrac13 \right)^{n-1}$

$\sqrt3, \nfrac{\sqrt3}{3}, \nfrac{\sqrt3}{9}, \nfrac{\sqrt3}{27}$

$a_n=\sqrt3 \left(- \nfrac13 \right)^{n-1}$

$\sqrt3, -\nfrac{\sqrt3}{3}, \nfrac{\sqrt3}{9}, -\nfrac{\sqrt3}{27}$

$a_n=-\sqrt3 \left( \nfrac12 \right)^{n-1}$

$-\sqrt3, -\nfrac{\sqrt3}{2}, -\nfrac{\sqrt3}{4}, -\nfrac{\sqrt3}{8}$

$a_n=-\sqrt3 \left(- \nfrac12 \right)^{n-1}$

$-\sqrt3, \nfrac{\sqrt3}{2}, -\nfrac{\sqrt3}{4}, \nfrac{\sqrt3}{8}$

$a_n=-\sqrt3 \left( \nfrac13 \right)^{n-1}$

$-\sqrt3, -\nfrac{\sqrt3}{3}, -\nfrac{\sqrt3}{9}, -\nfrac{\sqrt3}{27}$

$a_n=-\sqrt3 \left(- \nfrac13 \right)^{n-1}$

$-\sqrt3, \nfrac{\sqrt3}{3}, -\nfrac{\sqrt3}{9}, \nfrac{\sqrt3}{27}$







[Level5]
()

$-3C-3$

$-3, 9, -27, 81$

$-3C-2$

$-3, 6, -12, 24$

$-3C-1$

$-3, 3, -3, 3$

$-3C2$

$-3, -6, -12, -24$

$-3C3$

$-3, -9, -27, -81$

$-2C-3$

$-2, 6, -18, 54$

$-2C-2$

$-2, 4, -8, 16$

$-2C-1$

$-2, 2, -2, 2$

$-2C2$

$-2, -4, -8, -16$

$-2C3$

$-2, -6, -18, -54$

$-1C-3$

$-1, 3, -9, 27$

$-1C-2$

$-1, 2, -4, 8$

$-1C-1$

$-1, 1, -1, 1$

$-1C2$

$-1, -2, -4, -8$

$-1C3$

$-1, -3, -9, -27$

$1C-3$

$1, -3, 9, -27$

$1C-2$

$1, -2, 4, -8$

$1C-1$

$1, -1, 1, -1$

$1C2$

$1, 2, 4, 8$

$1C3$

$1, 3, 9, 27$

$2C-3$

$2, -6, 18, -54$

$2C-2$

$2, -4, 8, -16$

$2C-1$

$2, -2, 2, -2$

$2C2$

$2, 4, 8, 16$

$2C3$

$2, 6, 18, 54$

$3C-3$

$3, -9, 27, -81$

$3C-2$

$3, -6, 12, -24$

$3C-1$

$3, -3, 3, -3$

$3C2$

$3, 6, 12, 24$

$3C3$

$3, 9, 27, 81$




[Level6]
()

$-3C\nfrac12$

$-3, -\nfrac32, -\nfrac34, -\nfrac38$

$-3C-\nfrac12$

$-3, \nfrac32, -\nfrac34, \nfrac38$

$-3C\nfrac13$

$-3, -1, -\nfrac13, -\nfrac19$

$-3C-\nfrac13$

$-3, 1, -\nfrac13, \nfrac19$

$-2C\nfrac12$

$-2, -1, -\nfrac12, -\nfrac14$

$-2C-\nfrac12$

$-2, 1, -\nfrac12, \nfrac14$

$-2C\nfrac13$

$-2, -\nfrac23, -\nfrac29, -\nfrac{2}{27}$

$-2C-\nfrac13$

$-2, \nfrac23, -\nfrac29, \nfrac{2}{27}$

$-1C\nfrac12$

$-1, -\nfrac12, -\nfrac14, -\nfrac18$

$-1C-\nfrac12$

$-1, \nfrac12, -\nfrac14, \nfrac18$

$-1C\nfrac13$

$-1, -\nfrac13, -\nfrac19, -\nfrac{1}{27}$

$-1C-\nfrac13$

$-1, \nfrac13, -\nfrac19, \nfrac{1}{27}$

$1C\nfrac12$

$1, \nfrac12, \nfrac14, \nfrac18$

$1C-\nfrac12$

$1, -\nfrac12, \nfrac14, -\nfrac18$

$1C\nfrac13$

$1, \nfrac13, \nfrac19, \nfrac{1}{27}$

$1C-\nfrac13$

$1, -\nfrac13, \nfrac19, -\nfrac{1}{27}$

$2C\nfrac12$

$2, 1, \nfrac12, \nfrac14$

$2C-\nfrac12$

$2, -1, \nfrac12, -\nfrac14$

$2C\nfrac13$

$2, \nfrac23, \nfrac29, \nfrac{2}{27}$

$2C-\nfrac13$

$2, -\nfrac23, \nfrac29, -\nfrac{2}{27}$

$3C\nfrac12$

$3, \nfrac32, \nfrac34, \nfrac38$

$3C-\nfrac12$

$3, -\nfrac32, \nfrac34, -\nfrac38$

$3C\nfrac13$

$3, 1, \nfrac13, \nfrac19$

$3C-\nfrac13$

$3, -1, \nfrac13, -\nfrac19$

$\nfrac12C-3$

$\nfrac12, -\nfrac32, \nfrac92, -\nfrac{27}{2}$

$\nfrac12C-2$

$\nfrac12, -1, 2, -4$

$\nfrac12C-1$

$\nfrac12, -\nfrac12, \nfrac12, -\nfrac12$

$\nfrac12C2$

$\nfrac12, 1, 2, 4$

$\nfrac12C3$

$\nfrac12, \nfrac32, \nfrac92, \nfrac{27}{2}$

$\nfrac12C\nfrac12$

$\nfrac12, \nfrac14, \nfrac18, \nfrac{1}{16}$

$\nfrac12C-\nfrac12$

$\nfrac12, -\nfrac14, \nfrac18, -\nfrac{1}{16}$

$\nfrac12C\nfrac13$

$\nfrac12, \nfrac16, \nfrac{1}{18}, \nfrac{1}{54}$

$\nfrac12C-\nfrac13$

$\nfrac12, -\nfrac16, \nfrac{1}{18}, -\nfrac{1}{54}$

$-\nfrac12C-3$

$-\nfrac12, \nfrac32, -\nfrac92, \nfrac{27}{2}$

$-\nfrac12C-2$

$-\nfrac12, 1, -2, 4$

$-\nfrac12C-1$

$-\nfrac12, \nfrac12, -\nfrac12, \nfrac12$

$-\nfrac12C2$

$-\nfrac12, -1, -2, -4$

$-\nfrac12C3$

$-\nfrac12, -\nfrac32, -\nfrac92, -\nfrac{27}{2}$

$-\nfrac12C\nfrac12$

$-\nfrac12, -\nfrac14, -\nfrac18, -\nfrac{1}{16}$

$-\nfrac12C-\nfrac12$

$-\nfrac12, \nfrac14, -\nfrac18, \nfrac{1}{16}$

$-\nfrac12C\nfrac13$

$-\nfrac12, -\nfrac16, -\nfrac{1}{18}, -\nfrac{1}{54}$

$-\nfrac12C-\nfrac13$

$-\nfrac12, \nfrac16, -\nfrac{1}{18}, \nfrac{1}{54}$

$\nfrac13C-3$

$\nfrac13, -1, 3, -9$

$\nfrac13C-2$

$\nfrac13, -\nfrac23, \nfrac43, -\nfrac83$

$\nfrac13C-1$

$\nfrac13, -\nfrac13, \nfrac13, -\nfrac13$

$\nfrac13C2$

$\nfrac13, \nfrac23, \nfrac43, \nfrac83$

$\nfrac13C3$

$\nfrac13, 1, 3, 9$

$\nfrac13C\nfrac12$

$\nfrac13, \nfrac16, \nfrac{1}{12}, \nfrac{1}{24}$

$\nfrac13C-\nfrac12$

$\nfrac13, -\nfrac16, \nfrac{1}{12}, -\nfrac{1}{24}$

$\nfrac13C\nfrac13$

$\nfrac13, \nfrac19, \nfrac{1}{27}, \nfrac{1}{81}$

$\nfrac13C-\nfrac13$

$\nfrac13, -\nfrac19, \nfrac{1}{27}, -\nfrac{1}{81}$

$-\nfrac13C-3$

$-\nfrac13, 1, -3, 9$

$-\nfrac13C-2$

$-\nfrac13, \nfrac23, -\nfrac43, \nfrac83$

$-\nfrac13C-1$

$-\nfrac13, \nfrac13, -\nfrac13, \nfrac13$

$-\nfrac13C2$

$-\nfrac13, -\nfrac23, -\nfrac43, -\nfrac83$

$-\nfrac13C3$

$-\nfrac13, -1, -3, -9$

$-\nfrac13C\nfrac12$

$-\nfrac13, -\nfrac16, -\nfrac{1}{12}, -\nfrac{1}{24}$

$-\nfrac13C-\nfrac12$

$-\nfrac13, \nfrac16, -\nfrac{1}{12}, \nfrac{1}{24}$

$-\nfrac13C\nfrac13$

$-\nfrac13, -\nfrac19, -\nfrac{1}{27}, -\nfrac{1}{81}$

$-\nfrac13C-\nfrac13$

$-\nfrac13, \nfrac19, -\nfrac{1}{27}, \nfrac{1}{81}$




[Level7]
([g)

$\sqrt2C-3$

$\sqrt2, -3\sqrt2, 9\sqrt2, -27\sqrt2$

$\sqrt2C-2$

$\sqrt2, -2\sqrt2, 4\sqrt2, -8\sqrt2$

$\sqrt2C-1$

$\sqrt2, -\sqrt2, \sqrt2, -\sqrt2$

$\sqrt2C2$

$\sqrt2, 2\sqrt2, 4\sqrt2, 8\sqrt2$

$\sqrt2C3$

$\sqrt2, 3\sqrt2, 9\sqrt2, 27\sqrt2$

$\sqrt2C\sqrt2$

$\sqrt2, 2, 2\sqrt2, 4$

$\sqrt2C-\sqrt2$

$\sqrt2, -2, 2\sqrt2, -4$

$\sqrt2C\sqrt3$

$\sqrt2, \sqrt6, 3\sqrt2, 3\sqrt6$

$\sqrt2C-\sqrt3$

$\sqrt2, -\sqrt6, 3\sqrt2, -3\sqrt6$

$-\sqrt2C-3$

$-\sqrt2, 3\sqrt2, -9\sqrt2, 27\sqrt2$

$-\sqrt2C-2$

$-\sqrt2, 2\sqrt2, -4\sqrt2, 8\sqrt2$

$-\sqrt2C-1$

$-\sqrt2, \sqrt2, -\sqrt2, \sqrt2$

$-\sqrt2C2$

$-\sqrt2, -2\sqrt2, -4\sqrt2, -8\sqrt2$

$-\sqrt2C3$

$-\sqrt2, -3\sqrt2, -9\sqrt2, -27\sqrt2$

$-\sqrt2C\sqrt2$

$-\sqrt2, -2, -2\sqrt2, -4$

$-\sqrt2C-\sqrt2$

$-\sqrt2, 2, -2\sqrt2, 4$

$-\sqrt2C\sqrt3$

$-\sqrt2, -\sqrt6, -3\sqrt2, -3\sqrt6$

$-\sqrt2C-\sqrt3$

$-\sqrt2, \sqrt6, -3\sqrt2, 3\sqrt6$

$\sqrt3C-3$

$\sqrt3, -3\sqrt3, 9\sqrt3, -27\sqrt3$

$\sqrt3C-2$

$\sqrt3, -2\sqrt3, 4\sqrt3, -8\sqrt3$

$\sqrt3C-1$

$\sqrt3, -\sqrt3, \sqrt3, -\sqrt3$

$\sqrt3C2$

$\sqrt3, 2\sqrt3, 4\sqrt3, 8\sqrt3$

$\sqrt3C3$

$\sqrt3, 3\sqrt3, 9\sqrt3, 27\sqrt3$

$\sqrt3C\sqrt2$

$\sqrt3, \sqrt6, 2\sqrt3, 2\sqrt6$

$\sqrt3C-\sqrt2$

$\sqrt3, -\sqrt6, 2\sqrt3, -2\sqrt6$

$\sqrt3C\sqrt3$

$\sqrt3, 3, 3\sqrt3, 9$

$\sqrt3C-\sqrt3$

$\sqrt3, -3, 3\sqrt3, -9$

$-\sqrt3C-3$

$-\sqrt3, 3\sqrt3, -9\sqrt3, 27\sqrt3$

$-\sqrt3C-2$

$-\sqrt3, 2\sqrt3, -4\sqrt3, 8\sqrt3$

$-\sqrt3C-1$

$-\sqrt3, \sqrt3, -\sqrt3, \sqrt3$

$-\sqrt3C2$

$-\sqrt3, -2\sqrt3, -4\sqrt3, -8\sqrt3$

$-\sqrt3C3$

$-\sqrt3, -3\sqrt3, -9\sqrt3, -27\sqrt3$

$-\sqrt3C\sqrt2$

$-\sqrt3, -\sqrt6, -2\sqrt3, -2\sqrt6$

$-\sqrt3C-\sqrt2$

$-\sqrt3, \sqrt6, -2\sqrt3, 2\sqrt6$

$-\sqrt3C\sqrt3$

$-\sqrt3, -3, -3\sqrt3, -9$

$-\sqrt3C-\sqrt3$

$-\sqrt3, 3, -3\sqrt3, 9$

$-3C\sqrt2$

$-3, -3\sqrt2, -6, -6\sqrt2$

$-3C-\sqrt2$

$-3, 3\sqrt2, -6, 6\sqrt2$

$-3C\sqrt3$

$-3, -3\sqrt3, -9, -9\sqrt3$

$-3C-\sqrt3$

$-3, 3\sqrt3, -9, 9\sqrt3$

$-2C\sqrt2$

$-2, -2\sqrt2, -4, -4\sqrt2$

$-2C-\sqrt2$

$-2, 2\sqrt2, -4, 4\sqrt2$

$-2C\sqrt3$

$-2, -2\sqrt3, -6, -6\sqrt3$

$-2C-\sqrt3$

$-2, 2\sqrt3, -6, 6\sqrt3$

$-1C\sqrt2$

$-1, -\sqrt2, -2, -2\sqrt2$

$-1C-\sqrt2$

$-1, \sqrt2, -2, 2\sqrt2$

$-1C\sqrt3$

$-1, -\sqrt3, -3, -3\sqrt3$

$-1C-\sqrt3$

$-1, \sqrt3, -3, 3\sqrt3$

$1C\sqrt2$

$1, \sqrt2, 2, 2\sqrt2$

$1C-\sqrt2$

$1, -\sqrt2, 2, -2\sqrt2$

$1C\sqrt3$

$1, \sqrt3, 3, 3\sqrt3$

$1C-\sqrt3$

$1, -\sqrt3, 3, -3\sqrt3$

$2C\sqrt2$

$2, 2\sqrt2, 4, 4\sqrt2$

$2C-\sqrt2$

$2, -2\sqrt2, 4, -4\sqrt2$

$2C\sqrt3$

$2, 2\sqrt3, 6, 6\sqrt3$

$2C-\sqrt3$

$2, -2\sqrt3, 6, -6\sqrt3$

$3C\sqrt2$

$3, 3\sqrt2, 6, 6\sqrt2$

$3C-\sqrt2$

$3, -3\sqrt2, 6, -6\sqrt2$

$3C\sqrt3$

$3, 3\sqrt3, 9, 9\sqrt3$

$3C-\sqrt3$

$3, -3\sqrt3, 9, -9\sqrt3$





[Level8]
([g)


$\nfrac12C\sqrt2$

$\nfrac12, \nfrac{\sqrt2}{2}, 1, \sqrt2$

$\nfrac12C-\sqrt2$

$\nfrac12, -\nfrac{\sqrt2}{2}, 1, -\sqrt2$

$\nfrac12C\sqrt3$

$\nfrac12, \nfrac{\sqrt3}{2}, \nfrac32, \nfrac{3\sqrt3}{2}$

$\nfrac12C-\sqrt3$

$\nfrac12, -\nfrac{\sqrt3}{2}, \nfrac32, -\nfrac{3\sqrt3}{2}$

$-\nfrac12C\sqrt2$

$-\nfrac12, -\nfrac{\sqrt2}{2}, -1, -\sqrt2$

$-\nfrac12C-\sqrt2$

$-\nfrac12, \nfrac{\sqrt2}{2}, -1, \sqrt2$

$-\nfrac12C\sqrt3$

$-\nfrac12, -\nfrac{\sqrt3}{2}, -\nfrac32, -\nfrac{3\sqrt3}{2}$

$-\nfrac12C-\sqrt3$

$-\nfrac12, \nfrac{\sqrt3}{2}, -\nfrac32, \nfrac{3\sqrt3}{2}$

$\nfrac13C\sqrt2$

$\nfrac13, \nfrac{\sqrt2}{3}, \nfrac23, \nfrac{2\sqrt2}{3}$

$\nfrac13C-\sqrt2$

$\nfrac13, -\nfrac{\sqrt2}{3}, \nfrac23, -\nfrac{2\sqrt2}{3}$

$\nfrac13C\sqrt3$

$\nfrac13, \nfrac{\sqrt3}{3}, 1, \sqrt3$

$\nfrac13C-\sqrt3$

$\nfrac13, -\nfrac{\sqrt3}{3}, 1, -\sqrt3$

$-\nfrac13C\sqrt2$

$-\nfrac13, -\nfrac{\sqrt2}{3}, -\nfrac23, -\nfrac{2\sqrt2}{3}$

$-\nfrac13C-\sqrt2$

$-\nfrac13, \nfrac{\sqrt2}{3}, -\nfrac23, \nfrac{2\sqrt2}{3}$

$-\nfrac13C\sqrt3$

$-\nfrac13, -\nfrac{\sqrt3}{3}, -1, -\sqrt3$

$-\nfrac13C-\sqrt3$

$-\nfrac13, \nfrac{\sqrt3}{3}, -1, \sqrt3$

$\sqrt2C\nfrac12$

$\sqrt2, \nfrac{\sqrt2}{2}, \nfrac{\sqrt2}{4}, \nfrac{\sqrt2}{8}$

$\sqrt2C-\nfrac12$

$\sqrt2, -\nfrac{\sqrt2}{2}, \nfrac{\sqrt2}{4}, -\nfrac{\sqrt2}{8}$

$\sqrt2C\nfrac13$

$\sqrt2, \nfrac{\sqrt2}{3}, \nfrac{\sqrt2}{9}, \nfrac{\sqrt2}{27}$

$\sqrt2C-\nfrac13$

$\sqrt2, -\nfrac{\sqrt2}{3}, \nfrac{\sqrt2}{9}, -\nfrac{\sqrt2}{27}$

$-\sqrt2C\nfrac12$

$-\sqrt2, -\nfrac{\sqrt2}{2}, -\nfrac{\sqrt2}{4}, -\nfrac{\sqrt2}{8}$

$-\sqrt2C-\nfrac12$

$-\sqrt2, \nfrac{\sqrt2}{2}, -\nfrac{\sqrt2}{4}, \nfrac{\sqrt2}{8}$

$-\sqrt2C\nfrac13$

$-\sqrt2, -\nfrac{\sqrt2}{3}, -\nfrac{\sqrt2}{9}, -\nfrac{\sqrt2}{27}$

$-\sqrt2C-\nfrac13$

$-\sqrt2, \nfrac{\sqrt2}{3}, -\nfrac{\sqrt2}{9}, \nfrac{\sqrt2}{27}$

$\sqrt3C\nfrac12$

$\sqrt3, \nfrac{\sqrt3}{2}, \nfrac{\sqrt3}{4}, \nfrac{\sqrt3}{8}$

$\sqrt3C-\nfrac12$

$\sqrt3, -\nfrac{\sqrt3}{2}, \nfrac{\sqrt3}{4}, -\nfrac{\sqrt3}{8}$

$\sqrt3C\nfrac13$

$\sqrt3, \nfrac{\sqrt3}{3}, \nfrac{\sqrt3}{9}, \nfrac{\sqrt3}{27}$

$\sqrt3C-\nfrac13$

$\sqrt3, -\nfrac{\sqrt3}{3}, \nfrac{\sqrt3}{9}, -\nfrac{\sqrt3}{27}$

$-\sqrt3C\nfrac12$

$-\sqrt3, -\nfrac{\sqrt3}{2}, -\nfrac{\sqrt3}{4}, -\nfrac{\sqrt3}{8}$

$-\sqrt3C-\nfrac12$

$-\sqrt3, \nfrac{\sqrt3}{2}, -\nfrac{\sqrt3}{4}, \nfrac{\sqrt3}{8}$

$-\sqrt3C\nfrac13$

$-\sqrt3, -\nfrac{\sqrt3}{3}, -\nfrac{\sqrt3}{9}, -\nfrac{\sqrt3}{27}$

$-\sqrt3C-\nfrac13$

$-\sqrt3, \nfrac{\sqrt3}{3}, -\nfrac{\sqrt3}{9}, \nfrac{\sqrt3}{27}$






[EOF]

