Q. 64.3( 110 Votes )

If the sum of a certain number of terms of the A.P. 25, 22, 19, … is 116. Find the last term.

Answer :

Given terms of A.P. 25, 22, 19, …………..


Let the sum of n terms of the given A.P. be 116.


Sn = 116


First Term = a = 25, Common Difference = d = 22 – 19 = -3



Putting the value of a, d and Sn



116 × 2 = n [50 – 3n + 3]


232 = 53n – 3n2 3n2 – 53n + 232 = 0


3n2 – 24n – 29n + 232 = 0


3n (n – 8) – 29 (n – 8) = 0


(3n – 29) (n – 8) = 0


n = 8 or 29/3


n cannot be equal to 29/3. Therefore, n = 8


Last term = a8 = a + (n – 1)d


a8 = 25 + (8 – 1) × (-3) = 25 – 21


a8 = 4


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
Trigonometric SeriesTrigonometric SeriesTrigonometric Series45 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