Q. 144.2( 67 Votes )

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

Answer :

Given: The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128.


Let a, ar, ar2, ar3, ar4, ar5 be the terms of the G.P


Here a + ar +ar2 = 16 ( given that sum of first 3 terms is 16) -------–1


Also, ar3, ar4, ar5 = 128 ( given that sum of next 3 terms is 128)--------------–2


Divide eq –2 and eq –1


We get,




r3 = 8


r = 8


r = 2


Here a + ar + ar2 = 16


a × (1 + r + r2) = 16


a × (1 + 2 + (2)2) = 16


a × (1 + 2 + 4) = 16


a × (7) = 16


a =


The Sum of terms in G.P. is given by:


=


First term of the G.P is , common ratio of the G.P is 2 and Sum of n terms of the G.P is


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive quiz on inequalities involving AM and GMInteractive quiz on inequalities involving AM and GMInteractive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 2| Interactive Quiz: Sequence & SeriesCheck Your progress Part 2| Interactive Quiz: Sequence & SeriesCheck Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 1)Sequence & Series (Lecture 1)Sequence & Series (Lecture 1)56 mins
Sequence & Series (Lecture 5)Sequence & Series (Lecture 5)Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)Sequence & Series (Lecture 7)Sequence & Series (Lecture 7)37 mins
Use of sigma in finding sumUse of sigma in finding sumUse of sigma in finding sum42 mins
Quick Recap lecture of Sequence & SeriesQuick Recap lecture of Sequence & SeriesQuick Recap lecture of Sequence & Series56 mins
General Term of Miscellaneous progressionGeneral Term of Miscellaneous progressionGeneral Term of Miscellaneous progression46 mins
Improve your understanding of AP & GPImprove your understanding of AP & GPImprove your understanding of AP & GP27 mins
Geometric ProgressionGeometric ProgressionGeometric Progression58 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses