If r = 3 and the sum of 6 terms of the geometric series is 3640, what is the first term?

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Answer 1 · 2016-05-07T09:37:44

First term is $10$

In a geometric series, if $a$ is the first term and ratio between a term and its preceding term is $r$ , then sum of first $n$ terms ia given by

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

As $r=3$ and sum of first $6$ terms is $3640$ , we have

$a(3^6-1)/(3-1)=3640$

hence $a(729-1)/(3-1)=(axx728)/2=3640$

or $364a=3640$ and hence

$a=10$ .