Question

Write an equation for the nth term of this sequence: 1/8, 1/4, 1/2, 1..

Answer 1

`a_n=(1)/(8) (2^(n-1))`

Explanation:

This is a geometric sequence. You start with the first term, 1/8, then multiply it by 2 to get 1/4, then double that to get 1/2, etc.

The number you multiply by is called the common ratio. In this case, the common ratio is 2.

A formula for the general (nth) term is:
`a_n=a_1 r^(n-1)`.

`a_1=1/8\\r=2`

So the nth term is
`a_n=(1)/(8) (2^(n-1))`