Question

Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

Answer 1

`a_(n) = 32((1)/(4))^(n-1)`

Explanation:

The nth term of a geometric sequence is given by the following equation.

`a_(n+1) = ra_(n)`

In which r is the common ratio.

This can be expanded for the nth term in the following way:

`a_(n) = a_(1)r^(n-1)`

In which
`a_(1)` is the first term.

This means that for example:

`a_(3) = a_(1)r^(3-1)`

So

`a_(3) = a_(1)r^(2)`

`2 = a_(1)((1)/(4))^(2)`

`2 = (a_(1))/(16)`

`a_(1) = 32`

Then

`a_(n) = 32((1)/(4))^(n-1)`