Question

已知an为等比数列,前n项之和Sn=5^(n-1)+k,则k=?

Answer 1

Sn=5^(n-1)+k

Sn-1=5^(n-2)+k

an=sn-sn-1=5^(n-1)+k-(5^(n-2)+k)=4/5*5^(n-1)

a1=4/5 q=5

Sn=(a1-an*q)/(1-q)

=(4/5-4/5*5^(n-1)*5)/(1-5)=5^(n-1)-1/5

Sn=5^(n-1)+k

k=-1/5