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Multiple Choice Questions

381.
Let S_n denotes the sum of first n terms of an AP.If S₄ = - 34, S₅ = - 60 and S₆ = - 93, then the common difference and the first term of the AP are respectively

- 7, 2

7, - 4

7, - 2

- 7, - 2

- 7, 2

Given,

S_n = Sum of first n terms of an AP

Let a and d be the first term and common difference of an AP.

$∴ S_{4} = \frac{4}{2} [2 a + (4 - 1) d] = - 34 [∵ S_{n} = \frac{n}{2} [2 a + (n - 1) d]] \Rightarrow 2 a + 3 d = - 17 . . . (i) and S_{5} = \frac{5}{2} [2 a + (5 - 1) d] = - 60 \Rightarrow 2 a + 4 d = - 24 . . . (ii) On subtracting Eq . (i) from Eq . (ii), we get d = - 7 Then, from Eq . (i), 2 a - 21 = - 17 \Rightarrow 2 a = 4 \Rightarrow a = 2$