This is the basic and conceptual question from Chapter name- Arithmetic Progression

Chapter number- 9

Exercise 9.6

In this question we have been given an arithmetic progression. And we have to find its sum upto 22 terms

CBSE DHANPAT RAI publications

Class:- 10th

Solutions of CBSE Mathematics

Question 1( v)

Given A.P. has first term(a) = a + b,

Common difference(d) = (a – b) – (a + b) = -2b

and number of terms(n) = 22

So, Sum of A.P. = S

_{22}= n[2a + (n – 1)d] / 2= 22[2(a + b) + (22 – 1)(-2b)]/2

= 11{2(a + b) – 22b)

= 11(2a – 40b) = 22a – 440b

Hence, the sum of the first 22 terms of A.P. is 22a – 440b.