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?

1 Answer
Apr 18, 2018

The sum of any geometric sequence is:

s=a(1-r^n)/(1-r)a1rn1r

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

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

324.8=200(1-r^4)/(1-r)324.8=2001r41r

1.624=(1-r^4)/(1-r)1.624=1r41r

1.624-1.624r=1-r^41.6241.624r=1r4

r^4-1.624r+.624=0r41.624r+.624=0

r-(r^4-1.624r+.624)/(4r^3-1.624)rr41.624r+.6244r31.624

(3r^4-.624)/(4r^3-1.624)3r4.6244r31.624 we get...

.5, .388, .399, .39999999, .3999999999999999.5,.388,.399,.39999999,.3999999999999999

So the limit will be .4 or 4/10.4or410

Thus your common ratio is 4/10Thusyourcommonratiois410

check...

s(4)=200(1-(4/10)^4))/(1-(4/10))=324.8s(4)=200(1(410)4))1(410)=324.8