Question

How do you find the nth term rule for 10,15, 22.5, 33.75, 50.63?

Answer 1

You divide each member by the one before it.

Explanation:

You'll find that the answer `r=1.5` (`r` for ratio)
The first term is called `u_0=10`
So the `n`th term is called `u_(n-1)` and it takes `n-1` multiplications to get there from `u_0`, so:

`n`th term `=u_(n-1)=u_0xxr^(n-1)`

Or, in your case:
`n`th term`=u_(n-1)=10xx1.5^(n-1)`