Question

在等差数列{a_n}中,a₁=3,且a₁,a₄,a₁₀成等比数列,则a_n的通项公式为

A.a_n=2n+1                                      B.a_n=n+2

C.a_n=2n+1或a_n=3                               D.a_n=n+2或a_n=3

Answer 1

D  设公差为d,a₄=a₁+3d,a₁₀=a₁+9d,

由题知a₄²=a₁a₁₀,∴(a₁+3d)²=a₁(a₁+9d),a₁=3,解得d=0或1.

当d=0时a_n=3,当d=1时,a_n=3+(n-1)=n+2.