Question

已知數列{a_n}是公差為d的等差數列,且d≠0,數列{b_n}是公比為q的等比數列,且a₁=1,a₂=b₁,a₅=b₂,a₁₄=b₃,則d=______________,q=______________.

Answer 1

2  3

解析:由已知得b₁=a₂=1+d,b₂=a₅=1+4d,b₃=a₁₄=1+13d,∵b₁,b₂,b₃成等比數列,∴b₂²=b₁b₃,

即1+8d+16d²=1+14d+13d²,3d²-6d=0,d=2或d=0(舍).∴b₁=3,b₂=9,q==3.

即公差d=2,公比q=3.