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

Mar 22, 2016

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 $= {u}_{n - 1} = {u}_{0} \times {r}^{n - 1}$

$n$th term$= {u}_{n - 1} = 10 \times {1.5}^{n - 1}$