# How do I find the first term of a geometric sequence?

Nov 15, 2015

In geometric sequences there is a case of repeated multiplication

Look down for more

#### Explanation:

a,ar,ar^2.....,ar^(n-1
$- - - - n - - - -$

So the sum of the first n terms of sequence is ;

${S}_{n} = \frac{a \left(1 - {r}^{n}\right)}{1 - r}$

Now given you know r n and the sum you find a by re arranging

${a}_{n} = a {r}^{n - 1}$