Question

设等差数列an的前n项和为sn,已知a5=-3,S10=-40,若数列 a（bn）为等比数列,且b1=5,b2=8

Answer 1

a5=-3,S10=-40

Sn=na1+n(n-1)d/2

a5=a1+4d=-3

s10=10a1+45*d=-40

2a1+9d=-8

2a1+8d=-6 (a1+4d=-3)

d=-2

a1=5

an=5+(n-1)*(-2)=7-2n

a(b1)=a5=-3

a(b2)=a8=-9

q=3

a(bn)=a(b1)q^(n-1)=-3*3^(n-1)=-3^n=7-2bn

bn=(7+3^n)/2

Tn=7n/2+3(3^n-1)/4