JEE PYQ: Sequence And Series Question 59
Question 59 - 2019 (09 Jan Shift 1)
Let $a_1, a_2, \ldots, a_{30}$ be an A.P., $S = \sum_{i=1}^{30} a_i$ and $T = \sum_{i=1}^{15} a_{(2i-1)}$.
If $a_5 = 27$ and $S - 2T = 75$, then $a_{10}$ is equal to:
(1) 52
(2) 57
(3) 47
(4) 42
Show Answer
Answer: (1)
Solution
Since, $S - 2T = 75$
$\Rightarrow 30a_1 + 435d - 30a_1 - 420d = 75$
$\Rightarrow d = 5$
Also, $a_5 = 27 \Rightarrow a_1 + 4d = 27$
$\Rightarrow a_1 = 7$
Hence, $a_{10} = a_1 + 9d = 7 + 9 \times 5 = 52$
BETA
