JEE PYQ: Sequence And Series Question 22
Question 22 - 2020 (03 Sep Shift 1)
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:
(1) $\frac{1}{6}$
(2) $\frac{1}{5}$
(3) $\frac{1}{4}$
(4) $\frac{1}{7}$
Show Answer
Answer: (1)
Solution
Given $a = 3$ and $S_{25} = S_{40} - S_{25}$
$\Rightarrow 2S_{25} = S_{40}$
$\Rightarrow 2 \times \frac{25}{2}[6 + 24d] = \frac{40}{2}[6 + 39d]$
$\Rightarrow 25(6 + 24d) = 20(6 + 39d)$
$\Rightarrow 5(2 + 8d) = 4(2 + 13d)$
$\Rightarrow 10 + 40d = 8 + 52d$
$\Rightarrow d = \frac{1}{6}$
BETA
