等差书列{An}前n项和为Sn.若S9=18,Sn=240,A=30,那n的值为_?(注,那个是个系数)
\有18,17,16,15这四个选项.
人气:111 ℃ 时间:2020-03-29 18:01:40
解答
n=15
Sn=(ai+aj)n/2 (其中:i+j=n+1)
S9=9*a5=18
所以a5=2
Sn=(a5+a[n-4])n/2=16n=240
所以,n=15
Sn=(ai+aj)n/2(i+j=n+1)的证明:
Sn=(a1+an)n/2
而等差数列中:如果i+j=n+1
那么,ai+aj=an+a1
所以,Sn=(ai+aj)n/2
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