Question

在数列{an}中,前n项和Sn=3^n+p(p为常数),若{an}是以q为公比的等比数列,则p+q为?

Answer 1

a(1)=s(1)=3+p,

s(n+1)=3^(n+1)+p,

a(n+1)=s(n+1)-s(n)=3^(n+1)-3^n=2*3^n,

a(1)=3+p,

a(n)=2*3^(n-1),n=2,3,...

a(2)=2*3=6,

q=a(2)/a(1)=6/(3+p)=a(3)/a(2)=3,

6=3(3+p),2 = 3+p,p=-1.

p+q=-1+3=2