Question

What is the formula for the nth term of the sequence 2,4,8,16,32

Answer 1

Below in bold.

Explanation:

4/2 = 2

8/4 = 2

Each term is obtained by multiplying the previous one by 2.

This is a geometric sequence with common ratio r = 2

the nth term

= a1r^(n-1) where a1 = the first term

= 2(2)^(n-1).

Answer 2

`a_(n) = 2_(n)`

Explanation:

`a_(1) = 2`

`d = a_(2) - a_(1)`

`= 4 - 2 = > 2`

Getting the nth term

`a_(n) = a_(1) + (n - 1)d`

`a_(n) = 2 + (n - 1)2`

`a_(n) = 2 + (2n - 2)`

`a_(n) = 2 + 2n - 2`

`a_(n) = 2n`