设等差数列{An}的前n项和为S
设等差数列{An}的前n项和为Sn,已知A3 = 16,S6 = 105,则S10 = ? 等差和等比数列通项公式分别是什么?
解:
A3 = A1 + 2d = 16
A6 = A1 + 5d = 16 + 3d
S6 = (A1 + A6)×6/2 = (A1 + 16 + 3d)×6/2 = 105
求得 A1 = 10,d = 3
而A10 = A1 + 9d = 10 + 27 = 37
所以 S10 = (A1 + A10)×10/2 = (10 + 37)×10/2 = 235
如下是等差、等比数列的通项公式。 全部
设等差数列{An}的前n项和为Sn,已知A3 = 16,S6 = 105,则S10 = ? 等差和等比数列通项公式分别是什么?
解:
A3 = A1 + 2d = 16
A6 = A1 + 5d = 16 + 3d
S6 = (A1 + A6)×6/2 = (A1 + 16 + 3d)×6/2 = 105
求得 A1 = 10,d = 3
而A10 = A1 + 9d = 10 + 27 = 37
所以 S10 = (A1 + A10)×10/2 = (10 + 37)×10/2 = 235
如下是等差、等比数列的通项公式。
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