JEE PYQ: Sequence And Series Question 5
Question 5 - 2021 (18 Mar Shift 1)
If $\alpha, \beta$ are natural numbers such that $100^\alpha - 199\beta = (100)(100) + (99)(101) + (98)(102) + \ldots + (1)(199)$, then the slope of the line passing through $(\alpha, \beta)$ and origin is:
(1) 540
(2) 550
(3) 530
(4) 510
Show Answer
Answer: (2)
Solution
$S = (100)(100) + (99)(101) + (98)(102) \ldots + (1)(199)$
$S = \sum_{x=0}^{99}(100 - x)(100 + x) = \sum 100^2 - x^2$
$= 100^3 - \frac{99 \times 100 \times 199}{6}$
$\alpha = 3$, $\beta = 1650$
slope $= \frac{1650}{3} = 550$
BETA
