Question

已知数列{an}的前n项和Sn=5^n+t,则{an}为等比数列的充要条件是

Answer 1

an=Sn-Sn-1

=5^n+t-(5^(n-1)+t)

=4*5^(n-1) (n≥2)

当n=1 时 a1=S1=5+t,

{an}为等比数列, 当n=1时,4*5^(n-1)的取值是4,

它应等于5+t,所以t=-1.