已知递增的等差数列{an}中,a1+a3=8,a3乘a6=72,求a1,d,an,Sn

问题描述:

已知递增的等差数列{an}中,a1+a3=8,a3乘a6=72,求a1,d,an,Sn

a1+a3=82a2=8a2=4a3=4+da6=4+4da3×a6=(4+d)(4+4d)=72(4+d)(1+d)=18d²+5d+4=18d²+5d-14=0(d-2)(d+7)=0d=2或d=-7 (舍去,因为是递增的等差数列)所以a1=a2-d=4-2=2d=2an=a1+(n-1)d=2+2(n-1)=2nsn=(a1+an)...