Question

已知等差数列an的公差不为零,a1=32,且a1,a9,a11成等比数列.求a4＋a7＋a11+……＋a3n+1

Answer 1

a1,a9,a11成等比数列，所以a9^2=a1a11,(32+8d)^2=32（32+10d),解得d=-3 an=32+(n-1)(-3)=35-3n a4＋a7＋a11+……＋a3n+1=(a4+a3n+1)n/2=(35-3*4+35-3*(3n+1))n/2=(55-9n*2)/2(a4,a7,a11,……,a3n+1是一个新的等差数列，首项a4公差是-12）