# Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

To find : n such that an = a54 + 132
Given:  a = 3, d = 15 – 3 = 12

nth term of an AP is given by:
an = a + (n - 1) d
where,
a = first term of AP
n = no. of terms of AP
d = common difference of AP

54th term can be given as follows:

a54 = a + ( 54 - 1)d

= 3 + 53 x 12

= 3 + 636
= 639

In question we have to find the term which is 132 more than 639 i.e. 771
Now an = 771, n = ?
Again applying the formula of nth term

771 = a + (n – 1)d

771 = 3 + (n -1)12

(n – 1)12 = 771 – 3 = 768

n - 1 = 768/12

n – 1 = 64

n = 65

Thus, the required term is 65th term.

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 