Q. 75.0( 2 Votes )

The sum of the first q terms of an AP is 63q–3q2. If its pth term is –60. Find the value of p. Also, find the 11th term of this AP.

Answer :

Let the first term be ‘a’ and common difference be ‘d’.


Given, Sum of q terms:


Sq = 63q – 3q2


pth term = Sum of p terms – Sum of (p – 1) terms


–60 = 63p – 3p2 – (63(p – 1) – 3(p – 1)2)


–60 = 63p – 3p2 – (63p – 63 – 3(p2 – 2p + 1))


–60 = 63p – 3p2 – (63p – 63 – 3p2 + 6p – 3)


–60 = 63p – 3p2 – 63p + 63 + 3p2 – 6p + 3


–60 = –6p + 66


6p = 126


p = 31


Also,


a11 = S11 – S10


a11 = 63(11) – 3(11)2 – (63(10) – 3(10)2)


a11 = 693 – 363 – 630 + 300


a11 = 0


Hence, 11th term is 0.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Arithmetic Progression34 mins
Champ Quiz | Arithmetic Progression30 mins
Lets Check Your Knowledge in A.P.49 mins
NCERT | Fundamental Theorem Of Arithmetic45 mins
Quiz on Arithmetic Progression Quiz32 mins
Fundamental Theorem of Arithmetic- 143 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Arithmetic Progression Tricks and QUIZ37 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
view all courses