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?

Question

4240 views around the world

You can reuse this answer
Creative Commons License

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#