a-math question

1. consider the equence {a(n)}. it is known that
a(1)=3, a(2)=5, and a(k)=3a(k-1)-2a(k-2)
prove by mathematical induction that a(n)= 2^n+1

2.if {a(n)}is asequence defined by a(1)=1, and a(n+1)=a(n)+n
prove that a(n)=(1/2)(n)(n-1)+1for all positive integers n