等比数列前n项和教学设计第二课时(最新整理)

等差数列前 n 项和性质：

性质 1：若 S n 是等比数列{a n }的前 n 项和，则数列 S n ,S 2n -S n ,S 3n -S 2n ……也构成等比数列。

【例 1】等比数列前 n 项和为 54，前 2n 项和为 60，则前 3n 项和为？

高一数学集体备课学案与教学设计

【练习 1】正项等比数列中，前 2 项和是 7，前 6 项和是 91，则前 4 项和是多少？

性质 2：在等比数列中，若项数为偶数(设 2n)，则 S 偶：S 奇=q

【例 2】已知一个等比数列项数是偶数，奇数项和是 85，偶数项和是 170，这个 数列的公比是多少？

【练习 2】已知一个等比数列其首项是 1，项数是偶数，奇数项和是 85，偶数项 和是 170，这个数列的项数是？

性质 3：若{a } 是公比为 q 的等比数列，则 S n n

m

n = S q n S m

【例 3】在等比数列{a n }中，前 3 项和为 7，前 8 项和为 255，且公比为 2，求前 11 项和.

性质 4：公比不为 1 的等比数列， S = A - Aq n

,

n A = a 1

1 - q

【例 4】等比数列{a }的前 n 项和S = 2 ⨯ 3n

+ a ，则 a 为？ n n

【练习 4】在等比数列{a } 中，已知对n ∈ N , a + a *

+ ⋅⋅⋅

+ a n = 2 -1 ，求 n n 1 2 a 2 + a 2 + ⋅⋅⋅ + a 2

1 2 n 【练习 5】求数列1, a + a 2 , a 3+ a 4 + a 5 ,⋅⋅⋅ 的前 n 项和

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