Give the recursive formula for the series 4,16,64...
0 solutions

16, the 2nd term, is 4 times the first term 4
64, the 3rd term, is 4 times the second term 16

So apparently,

Each term = 4 times the previous term

There are two acceptable ways to write that sentence
as a recursion formula:

If you think of it as

The nth term is 4 times the (n-1)st term

then the recursion formula is

an = 4·an-1, a1 = 4 where n > 1

Or if you think of it as

The (n+1)st term is 4 times the nth term

then the recursion formula is

an+1 = 4·an, a1 = 4 where n > 0

They are both correct, and equivalent.

Edwin