設(shè)等比數(shù)列an的比為q
a1=1,a2=a1q=q
a5=a1q^4=q^4
a5=8a2=8a1q=8q
∴q^4=8q
∴q=2 an=a1q^(n-1)=2^(n-1)
bn=an+n=2^(n-1)+n
sn=b1+b2+b3+...+bn
=(1+1)+(2+2)+(4+3)+...2^(n-1)+n
=[1+2+4+...+2^(n-1)]+(1+2+3+...+n)
=(1-2^n)/(1-2)+(1+n)n/2=(n+n^2)/2-1+2^n