Question

已知等比数列{an}中a1=2,公比q满足lg3*log3(q)=lg2,试写出{an}的通项公式,

Answer 1

1.

an=2q^(n-1)

lg3*log3(q)=lg2

log3(q)=lg2/lg3=log3 (2)

q=2

an=2^n

2.

bn=a(n)+n=2^n+n

Sn=[2^1+1]+[2^2+2]+[2^3+3]+……+[2^(n-1)+(n-1)]+[2^n+n]

=[1+2+3+……+(n-1)+n]+[2^1+2^2+2^3+……+2^(n-1)+2^n]

=(n+1)n/2+2[2^n-1]/(2-1)

=(n+1)n/2+2^(n+1)-2