题目内容
设数列
是等比数列,
,已知
, (1)求数列
的首项和公比;(2)求数列
的通项公式。
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(1)
(2)
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本题主要考查了等比数列的通项公式的求解,数列求和的错位相减求和是数列求和中的重点与难点,要注意掌握。
(1)设等比数列{an}的公比为q,则q+q2=6,解方程可求q
(2)由(1)可求an=a1•qn-1=2n-1,结合数列的特点,考虑利用错位相减可求数列的和
解:(1)
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……4分
(2)
, ……5分
……6分
……8分
两式相减:
……12分
(1)设等比数列{an}的公比为q,则q+q2=6,解方程可求q
(2)由(1)可求an=a1•qn-1=2n-1,结合数列的特点,考虑利用错位相减可求数列的和
解:(1)
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(2)
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两式相减:
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