若等差数列{an}的首项a1=1,数列{bn}是等比数列,{an+bn}的前三项为3,12,23,
问题描述:
若等差数列{an}的首项a1=1,数列{bn}是等比数列,{an+bn}的前三项为3,12,23,
则{an}的公差d与{bn}的公比q之和为多少
答
a1+b1=3 1+b1=3b1=2a2+b2=12a1+d+b1q=121+d+2q=12d+2q=11a3+b3=23a1+2d+b1q^2=231+2d+2q^2=23d+q^2=11d+2q=d+q^2q^2-2q=0q(q-2)=0q=2或q=0(舍去)d+2*2=11d=7d+q=2+7=9