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?

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Answer 1 · 2018-04-18T20:41:40

The sum of any geometric sequence is:

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

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

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

$324.8=200(1-r^4)/(1-r)$

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

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

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

$r-(r^4-1.624r+.624)/(4r^3-1.624)$

$(3r^4-.624)/(4r^3-1.624)$ we get...

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

So the limit will be $.4 or 4/10$

$Thus your common ratio is 4/10$

check...

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