等比数列中,a3=3/2 S3=9/2 求a1及q

发布网友发布时间：2024-10-01 16:39

共1个回答

热心网友时间：2024-10-27 00:38

a(n) = aq^(n-1),
3/2 = a(3) = aq^2, a = 3/(2q^2).
9/2 = s(3) = a(1+q+q^2) = a(1+q) + aq^2 = a(1+q) + 3/2,
3 = a(1+q) = 3(1+q)/(2q^2),
2q^2 = 1+q,
0 = 2q^2 - q - 1 = (2q+1)(q-1),
q = -1/2或q=1.

q=-1/2时，a = 3/(2q^2) = 6.
q=1时，a = 3/(2q^2) = 3/2.

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