1, 1, 2, 3, 5, 8, ... is a recursive sequence, where:

a_{1}=1

a_{2}=1

a_{n}=a_{n-1}+a_{n-2}

(It is well known as The Fibonacci Sequence)

Given:

a

_{1}=1

a

_{2}=2

a

_{n}=2a

_{n-1}+a

_{n-2}
Find the next three terms.

a_{3}=2a_{2}+a_{1}=2(2)+1=5

a_{4}=2a_{3}+a_{2}=2(5)+2=12

a_{5}=2a_{4}+a_{3}=2(12)+5=29