Question

How do you find a formula for the nth term of the geometric sequence: 8, 12, 18, 27, ...?

Answer 1

`n`th term is `8*(3/2)^(n-1)`

Explanation:

The formula for `n`th term of geometric sequence is `a_1q^(n-1)`, where `a_1` is the 1st term and `q` is the quotient of this sequence (check for `n=1`).

To find quotien `q` we must divide any term by its previous one - result will be the same (it's geometric sequence definition).

`q=a_k/a_(k-1)=a_2/a_1=12/8=3/2` for any `k>1`.

Moreover

`12/8=18/12=27/18=...`

so the sequence is geometric indeed.

...

Fun fact: next term is not an integer.