已知等比数列an的前n项和为Sn=a2^n-1+1⼀6,则a的值为?

2025-04-14 22:28:58
推荐回答(2个)
回答(1):

Sn=a2^﹙n-1﹚ 1/6
an=Sn-S﹙n-1﹚
=a2^﹙n-1﹚-a2^﹙n-2﹚
a1=a-a/2=a/2=S1=a 1/6
∴a=﹣1/3

回答(2):

Sn=a2^﹙n-1﹚+1/6
an=Sn-S﹙n-1﹚
=a2^﹙n-1﹚-a2^﹙n-2﹚
a1=a-a/2=a/2=S1=a+1/6
∴a=﹣1/3


Sn=a1﹙1-q^n﹚/﹙1-q﹚
Sn=a2^﹙n-1﹚+1/6
=a/2·﹙2^n-1﹚+1/6+a/2

∴1/6+a/2=0

∴a=﹣1/3