# How many terms of the AP 21, 18, 15, ... must be added to get the sum 0?

Here, first term = a = 21

Common difference = d = 18 - 21 = - 3

Let first n terms of the AP sums to zero.

Sn = 0

To find: n

Now, Sn = (n/2) × [2a + (n - 1)d]

Since, Sn = 0

(n/2) × [2a + (n - 1)d] = 0

(n/2) × [2(21) + (n - 1)(-3)] = 0

(n/2) × [42 - 3n + 3)] = 0

(n/2) × [45 - 3n] = 0

[45 - 3n] = 0

45 = 3n

n = 15

15 terms of the given AP sums to zero.

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  Arithmetic progression: Previous Year NTSE Questions34 mins  Quiz on Arithmetic Progression Quiz32 mins  Arithmetic Progression Tricks and QUIZ37 mins  Quiz | Group of Questions on General Term of an A.P49 mins  Become a Master of A.P. in 45 Minutes!!47 mins  Get to Know About Geometric Progression41 mins  NCERT | Solving Questions on Introduction of A.P42 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 