Question

a. Find the recursive definition for the sequence

i. 2 , 4 , 16 , 256 , ......

ii. 1 , 5 , 52 , 53 , 54 , ...

Answer 1

i. $2, 2^2, 4^2, 16^2,...$

$$a_1=2,a_{n}=a_{n-1}^2, n>1$$

ii. $a_1=1, a_2=5, a_n=10a_2+a_1(n-1), n\geq3$