题目

关于等差数列与等比数列
1.在等差数列｛an｝中,Sp=q,Sq=q,则Sp+q的值为
2.已知等差数列3,7,11…,139与2,9,16…,142则它们所有公共项的个数为多少?
3.已知等差数列｛an｝前三项的和为-3,前三项的积为8,若a2,a3,a1成等比数列,求｛an｝的前n项和

提问时间：2020-11-23

答案

(1).Sp = (A1+Ap)*p/2 = [2A1+(p-1)d]*p/2 = pA1 +p(p-1)d/2 = pA1 +p^2*d/2 -pd/2 = q Sq = (A1+Aq)*q/2 = [2A1+(q-1)d]*q/2 = qA1 +q(q-1)d/2 = qA1 +q^2*d/2 -qd/2 = p两式相减：(p-q)A1 +(p+q)(p-q)d/2 -(p-q)d/...