Question

设等比数列{a_n}的公比为q,前n项和为S_n.若S_n+1,S_n,S_n+2成等差数列,则q的值为______.

Answer 1

-2

解析:当q=1时,S_n=na₁,

∴2S_n=S_n+1+S_n+2.

即2na₁=(n+1)a₁+(n+2)a₁.

∴a₁=0(舍).

当q≠1时,S_n=.

∴,

即q²+q-2=0.

∴q=-2或1(舍).

∴q=-2.