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 of first 51 terms of the A.P. : whose second term is 2 and fourth term is 8.

CBSE DHANPAT RAI publications

Class:- 10th

Solutions of CBSE Mathematics

Question 11(iii)

Given A.P. has second term(a

_{2}) = 2,Fourth term(a

_{4}) = 8 andnumber of terms(n) = 51.

=> a

_{2}= a + d=> 2 = a + d …(1)

Also, a

_{4}= a + 3d=> 8 = a + 3d … (2)

Subtracting (1) from (2), we have

=> 2d = 6

=> d = 3

Putting d = 3 in (1), we get a = −1.

We know sum of n terms of an A.P. is given by, S

_{n}= n[2a + (n − 1)d] / 2.S

_{51}= 51[2(−1) + (51 − 1)(3)]/2= 51[−2 + 150]/2

= 51[74] = 3774

Hence, the sum of first 51 terms of the given A.P. is 3774.