Question

How do you find nth term rule for `a_1=1/4` and `a_3=6`?

Answer 1

The formula for the `n`th term is one of the following:

`a_n = 1/4 (2sqrt(6))^(n-1)`

`a_n = 1/4 (-2sqrt(6))^(n-1)`

Explanation:

Assuming this is a geometric sequence...

The general term of a geometric sequence is given by the formula:

`a_n = ar^(n-1)`

where `a` is the initial term and `r` the common ratio.

So we have `a = a_1 = 1/4` and we find:

`r^2 = (ar^2)/(ar^0) = a_3/a_1 = 6/(1/4) = 24`

So:

`r = +-sqrt(24) = +-2sqrt(6)`

So the formula for the `n`th term is one of the following:

`a_n = 1/4 (2sqrt(6))^(n-1)`

`a_n = 1/4 (-2sqrt(6))^(n-1)`