设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.

设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.
设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.

设等比数列{an}的前n项和为Sn,已知a2=6,6a1+a3=30,求an和Sn.
A2=6 A1q=6
6A1＋A3 6A1＋A1q²=30
q/(6＋q²)=1/5
q²－5q＋6=0
a=2或q=3
当q=2时,A1=3,则：An=A1q^(n－1)=3×2^(n－1)
Sn=[A1(1－q^n)]/[1－q]=3[2^(n)－1]
当q=3时,A1=2,则An=A1q^(n－1)=2×3^(n－1)
Sn=[A1(1－q^n)]/[1－q]=3^n－1