数列前n项和为Sn=3*2^n +k,若它为等比数列,求k._数学解答

数列前n项和为Sn=3*2^n +k,若它为等比数列,求k.

人气：138 ℃　时间：2020-03-27 13:10:03

解答

sn-1=3*2^n-1 +k
an=sn-sn-1
=3*2^n +k-3*2^n-1 -k
=3*2^n-3*2^n-1
=3*2*2^n-1 -3*2^n-1
=3*2^n-1(2-1)
=3*2^n-1
a1=3*2^0=3
a1=s1=3*2+k=6+k
3=6+k
k=-3