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(a2) = 2,
Fourth term(a4) = 8 and
number of terms(n) = 51.
=> a2 = a + d
=> 2 = a + d …(1)
Also, a4 = 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, Sn = n[2a + (n − 1)d] / 2.
S51 = 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.