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数学
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等差数列an中,a1+a2+.+a50=200,a51+a52+...+a100=2700,则a1的值为?
人气:301 ℃ 时间:2020-01-30 01:51:47
解答
分析:根据条件所给的两个等式相减,得到数列的公差,再根据前50项的和是200,代入求和公式做出首项,题目给出的这样的条件,可以解决等差数列的一系列问题.
∵a1+a2+…+a50=200 ①
a51+a52+…+a100=2700 ②
②-①得:50×50d=2500,
∴d=1,
∵a1+a2+…+a50=200,
∴na1+ n(n+1)d/2=200,
∴50a1+25×51=200,
∴a1=-20.5,
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