# The first term of a geometric sequence is 200 and the sum of the first four terms is 324.8. How do you find the common ratio?

Apr 18, 2018

The sum of any geometric sequence is:

s=$a \frac{1 - {r}^{n}}{1 - r}$

s=sum, a=initial term, r=common ratio, n=term number...

We are given s, a, and n, so...

$324.8 = 200 \frac{1 - {r}^{4}}{1 - r}$

$1.624 = \frac{1 - {r}^{4}}{1 - r}$

$1.624 - 1.624 r = 1 - {r}^{4}$

${r}^{4} - 1.624 r + .624 = 0$

$r - \frac{{r}^{4} - 1.624 r + .624}{4 {r}^{3} - 1.624}$

$\frac{3 {r}^{4} - .624}{4 {r}^{3} - 1.624}$ we get...

$.5 , .388 , .399 , .39999999 , .3999999999999999$

So the limit will be $.4 \mathmr{and} \frac{4}{10}$

$T h u s y o u r c o m m o n r a t i o i s \frac{4}{10}$

check...

s(4)=200(1-(4/10)^4))/(1-(4/10))=324.8