Question

How do you find nth term rule for `2,8,32,128,...`?

Answer 1

`a_n = 2^(2n-1)`

Explanation:

Consider the given sequence: 2, 8, 32, 128, ...

Notice that each term is an odd power of 2:

`a_1 = 2 = 2^1`
`a_2 = 8 = 2^3`
`a_3 = 32 = 2^5`
`a_4 = 128 = 2^7`

In general the sequence of the odd naturals is generated by: `i = (2n-1) forall n in NN`

Hence our general term is: `a_n = 2^(2n-1)`