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#