已知等差数列{an},a1＝4,又a1,a7,a10成等比数列,若前几项和sn＝11,求n

Question

已知等差数列{an},a1＝4,又a1,a7,a10成等比数列,若前几项和sn＝11,求n

Answer 1

a7*a7=a1*a10
(a1+6d)(a1+6d)=a1(a1+9d)
a1^2+12a1d+36d^2=a1^2+9a1d
a1=-12d
a1=4 d=-1/3
Sn=na1+n(n-1)d/2
11=4n+n(n-1)(-1/6)
n^2-25n+66=0
n=3或n=22
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