JEE PYQ: Sequence And Series Question 38
Question 38 - 2020 (07 Jan Shift 2)
If the sum of the first 40 terms of the series, $3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \ldots$ is $(102)m$, then $m$ is equal to:
(1) 20
(2) 25
(3) 5
(4) 10
Show Answer
Answer: (1)
Solution
$S = 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 \ldots$ 40 terms
$S = 7 + 17 + 27 + 37 + 47 + \ldots$ 20 terms
$S_{40} = \frac{20}{2}[2 \times 7 + (19)(10)] = 10[14 + 190]$
$= 10(2040) = (102)(20)$
$\Rightarrow m = 20$
BETA
