Question

已知等比数列an中,a3-a1=15,a2-a1=5,则s5等于

Answer 1

设公本比为q,

a3-a1=a1q^2-a1=15

a1(q^2-1)=15 (1).

a2-a1=(a1(q-1)=5.

a1(q-1)=5 (2).

(1)/(2),得:q+1=3.

q=2,a1=5.

S5=a1(q^5-1)/(q-1).

=5*(2^5-1)/(2-1).

=5*(32-1).

=5*31.

∴S5=155.