Find the next three terms of the recursively defined sequence. a1 = 3, a2 = -1, ak+2 = ak+1ak

Question

 Find the next three terms of the recursively defined sequence. a1 = 3, a2 = −1, ak+2 = ak+1ak 

Answer 1

The sequence is specified as 

 

a₁=3

a₂=-1

 

a_k+2=a_k+1+a_k

 

The next three terms are a₃, a₄, and a₅

 

These terms correspond to k=1, 2, and 3.

 

k=1:    a₃=a₂+a₁=-1+3=2

 

k=2:    a₄=a₃+a₂=2-1=1

 

k=3:    a₅=a₄+a₃=1+2=3