Question

数列{an}中,a1=3an+二的n次方,求{an}

Answer 1

a(n+1)=3an+2^n

a(n+1)+x*2^(n+1)=3(an+x*2^n)

a(n+1)=3an+3x*2^n-x*2*2^n

a(n+1)=3an+x*2^n

x=1

a(n+1)+2^(n+1)=3(an+2^n)

an+2^n=bn,b1=a1+2=4

b(n+1)=3bn

bn=4*3^(n-1)

an=4*3(n-1)-2^n