The sum of the first four terms of a geometric series is 130 and its common ratio is 1.5. What is the first term in the series?

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Answer 1 · 2016-03-24T07:20:48

First four terms of the series are $16, 24, 36, 54$

As common ratio is $1.5$ or $3/2$ , let the first four terms of the geometric series be $a, 3/2*a, (3/2)^2a, (3/2)^3a$ or

$a, 3/2a,9/4a$ and $27/8a$ .

Now there sum is $130$ , hence

$a+(3a)/2+(9a)/4+(27a)/8=130$ or

$(8a+12a+18a+27a)/8=130$ or

$(65a)/8=130$ or $a=2cancel(130)xx8/(1cancel(65))=16$

Hence first four terms of the series are

$16, 16xx3/2, 16xx9/4, 16xx27/8$ or

$16, 24, 36, 54$