Question

数列题,第（3）问

Answer 1

a1=2,a2=3

an=3a(n-1)-2a(n-2)

an-a(n-1)= 2(a(n-1) - a(n-2) )

=>{an-a(n-1)}是等比数列,q=2

an-a(n-1) = 2^(n-2). ( a2-a1)

=2^(n-2)

an-a2 = 2^1+2^2+...+2^(n-2)

= 2(2^(n-2) -1 )

an =1+ 2^(n-1)