JEE PYQ: Sequence And Series Question 57
Question 57 - 2019 (12 Apr Shift 2)
If $a_1, a_2, a_3, \ldots$ are in A.P. such that $a_1 + a_7 + a_{16} = 40$, then the sum of the first 15 terms of this A.P. is:
(1) 200
(2) 280
(3) 120
(4) 150
Show Answer
Answer: (1)
Solution
Let the common difference of the A.P. is ‘$d$’.
Given, $a_1 + a_7 + a_{16} = 40$
$\Rightarrow 3a_1 + 21d = 40$
$\Rightarrow a_1 + 7d = \frac{40}{3}$ …(i)
Now, sum of first 15 terms of this A.P. is,
$S_{15} = \frac{15}{2}[2a_1 + 14d] = 15(a_1 + 7d)$
$= 15\left(\frac{40}{3}\right) = 200$ [Using (i)]
BETA
