Q. 34.0( 155 Votes )

In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20th term is –112.

Answer :

Given, first term a = 2


Let d be the common difference


Let Sn denote sum of n terms,



tn denote nth term.


tn = a + (n – 1)d


S1 = Sum of first five terms.


S2 = Sum of next five terms.



S1 = 10 × (1 + d)


Sum of next 10 terms = Sum of first 10 terms - Sum of first 5 terms


S2 = 20 + 45d – 10 – 10d = 10 + 35d


Also, S1 = 1/4 S2


10 + 10d = 1/4 (10 + 35d)


40 + 40d = 10 + 35d


30 = -5d


d = -6


t20 = 2 + (20 – 1) × (-6)


t20 = 2 – 19 × 6 = 2 – 114


t20 = -112

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
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
Sequence & Series (Lecture 4)Sequence & Series (Lecture 4)Sequence & Series (Lecture 4)FREE Class
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