JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Sequences and Series

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If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is:

(A) $\frac{1}{4}$
(B) $\frac{1}{7}$
(C) $\frac{1}{6}$ ✓ Correct
(D) $\frac{1}{5}$

Answer: (C)

Solution

With first term

3

, the sum of the first

25

terms equalling the sum of the next

15

means

S_{40} = 2 S_{25}

. So

\frac{40}{2} (6 + 39 d) = 2 \cdot \frac{25}{2} (6 + 24 d)

, i.e.

120 + 780 d = 150 + 600 d

, giving

180 d = 30

and

d = \frac{1}{6}

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Single correct option

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