A Geometric Series has 8 terms whose sum of the first 3 terms is #13/9# and the sum of last 3 terms is #351#. Find the first term and the common ratio of the series.?

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Answer 1 · 2017-12-10T13:55:22

The common ratio is #=3# and the first term is#=1/9#

Let the terms of the geometric series be

#a, ar, ar^2,.......ar^5+ar^6+ar^7#

The sum of the first #3# terms is

#a+a+ar^2=13/9#

#a(1+r+r^2)=13/9#

The sum of the last #3# terms is

#ar^5+ar^6+ar^7 =351#

#ar^5(1+r+r^2)=351#

Therefore,

#ar^5(13/9)/a=351#

#r^5=9*351/13=9*27=3^5#

Therefore,

the common ratio is #r=3#

The first term is

#a=13/9*(1/(1+3+9))=1/9#