等比数列an的前n项和为Sn,已知S1,S3,S2,成等差数列,(1)求an的公比q
等比数列an的前n项和为Sn,已知S1,S3,S2,成等差数列,(1)求an的公比q(2)若a1-a3=3,求Sn...
等比数列an的前n项和为Sn,已知S1,S3,S2,成等差数列,(1)求an的公比q (2)若a1-a3=3,求Sn
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a(n) = aq^(n-1),
2s(3) = 2[a + aq + aq^2] = s(1)+s(2) = a + [a+aq] = 2a + aq,
0 = 2aq^2 + aq = aq(2q + 1),
q = -1/2.
3 = a(1)-a(3) = a - aq^2 = a - a/4 = 3a/4, a = 4.
a(n) = 4(-1/2)^(n-1),
s(n) = 4[1-(-1/2)^n]/(1+1/2) = (8/3)[ 1 - (-1/2)^n ]
2s(3) = 2[a + aq + aq^2] = s(1)+s(2) = a + [a+aq] = 2a + aq,
0 = 2aq^2 + aq = aq(2q + 1),
q = -1/2.
3 = a(1)-a(3) = a - aq^2 = a - a/4 = 3a/4, a = 4.
a(n) = 4(-1/2)^(n-1),
s(n) = 4[1-(-1/2)^n]/(1+1/2) = (8/3)[ 1 - (-1/2)^n ]
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