Question

一個(gè)項(xiàng)數(shù)為偶數(shù)的等比數(shù)列，它的偶數(shù)項(xiàng)和是奇數(shù)項(xiàng)和的2倍，又它的首項(xiàng)為1，且中間兩項(xiàng)的和為24，則此等比數(shù)列的公比為_________，項(xiàng)數(shù)為________.

Answer 1

2     8

解析:設(shè)項(xiàng)數(shù)為2n,由它的偶數(shù)項(xiàng)和是奇數(shù)項(xiàng)和的2倍知q=2,又a_n+a_n+1=24,即3a₁·2^n-1=24._?

∵a₁=1,_?

∴n=4,項(xiàng)數(shù)為8.