Question

What is the formula for the `n th` term for the example `6,12,24,48,96?`

please help with finding the pattern for the `n th` term for `6, 12, 24, 48, 96...`

Answer 1

`T_n = 6*2^(n-1)`

Explanation:

First establish whether it is arithmetic, geometric or neither,

`d= 24-12 = 12 and d= 12-6 =6" "` it is NOT arithmetic because `d` changes

`r =24div12 = 2 and r= 12div6 =2" "` it is geometric because `r` is the same. Each term is twice the term before it.

The Formula for the general term of a GP is `" "T_n=a r^(n-1)`

We have already found that `r=2`.

`a` is the first term, which is `6`.

Substitute these values into the general formula:

`T_n = 6*2^(n-1)`