中五數學

等比數列的首三項之和為16,而其後的三項之和為128.求等比數列的首項,公比及首n項的和.

(詳列部驟)

a+ar+ar^2 = 16
ar^3 + ar^4 + ar^5 = 128

所以 a(1 + r + r^2) = 16 ------(1)
ar^3(1 + r + r^2) = 128 ------(2)

(2) / (1)
r^3 = 8
r = 2

a(1 + 2 + 4) = 16
a = 16/7

S(n) = 16/7(2^ n - 1)/ (2 - 1)
= 16/7 (2^n - 1)

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