已知数列{an}满足a1=1,a的n+1=an+2的n次方,则a10=

Question

已知数列{an}满足a1=1,a的n+1=an+2的n次方,则a10=

Answer 1

a(n+1)=an+2^n
a(n+1)-2^(n+1)=an-2^n
a1-2^1=1-2=-1
数列{an-2^n}是各项均为-1的常数数列.
an-2^n=-1
an=2^n -1
a10=2^10-1=1023