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# Question 11. Find the sum of the first(iii) 51 terms of the A.P. : whose second term is 2 and fourth term is 8.

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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)

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1. Given A.P. has second term(a2) = 2,

Fourth term(a4) = 8 and

number of terms(n) = 51.

=> a2Â = a + d

=> 2 = a + d Â â€¦(1)

Also, a4Â = a + 3d

=> 8 = a + 3d Â â€¦ (2)

Subtracting (1) from (2), we have

=> 2d = 6

=> d = 3

Putting d = 3 in (1), we get a = âˆ’1.

We know sum of n terms of an A.P. is given by, SnÂ = n[2a + (n âˆ’ 1)d] / 2.

S51Â = 51[2(âˆ’1) + (51 âˆ’ 1)(3)]/2

= 51[âˆ’2 + 150]/2

= 51[74] = 3774

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

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