JEE PYQ: Sequence And Series Question 36
Question 36 - 2020 (07 Jan Shift 1)
Five numbers are in A.P., whose sum is 25 and product is 2520. If one of these five numbers is $-\frac{1}{2}$, then the greatest number amongst them is:
(1) 27
(2) 7
(3) $\frac{21}{2}$
(4) 16
Show Answer
Answer: (4)
Solution
Let 5 terms of A.P. be $a - 2d, a - d, a, a + d, a + 2d$.
Sum $= 25 \Rightarrow 5a = 25 \Rightarrow a = 5$
Product $= 2520$
$(5 - 2d)(5 - d) \cdot 5(5 + d)(5 + 2d) = 2520$
$(25 - 4d^2)(25 - d^2) = 504$
$4d^4 - 125d^2 + 121 = 0$
$(d^2 - 1)(4d^2 - 121) = 0$
$d = \pm 1, d = \pm \frac{11}{2}$, does not give $-\frac{1}{2}$ as a term
$\therefore d = \frac{11}{2}$
$\therefore$ Largest term $= 5 + 2d = 5 + 11 = 16$
BETA
