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#