# The 12th term of an AP is – 13 and the sum of its first four terms is 24. Find the sum of its first 10 terms.

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

Given: a12 = - 13

S4 = 24

To find: Sum of first 10 terms.

Consider a12 = - 13

a + 11d = - 13 ………………(1)

Also, S4 = 24

(4/2) × [2a + (4 - 1)d] = 24

2 × [2a + 3d] = 24

2a + 3d = 12 …………….(2)

Subtracting equation (2) from twice of equation (1), we get,

19d = - 38

d = - 2

Now, from equation (1), we get

a = - 13 - 11d

a = - 13 - 11(-2)

a = - 13 + 22

a = 9

Now, Sum of first n terms of this arithmetic series is given by:

Sn = [2a + (n - 1)d]

Therefore sum of first 10 terms of this arithmetic series is given by:

S10 = [2(9) + (10 - 1)(-2)]

= 5 × [18 - 18]

= 0

S10 = 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  Arithmetic progression: Previous Year NTSE Questions34 mins  Arithmetic Progression Tricks and QUIZ37 mins  Quiz | Group of Questions on General Term of an A.P49 mins  Quiz on Arithmetic Progression Quiz32 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 