JEE PYQ: Sequence And Series Question 49
Question 49 - 2019 (09 Apr Shift 2)
If the sum and product of the first three terms in an A.P. are 33 and 1155, respectively, then a value of its $11^{th}$ term is:
(1) $-35$
(2) 25
(3) $-36$
(4) $-25$
Show Answer
Answer: (4)
Solution
Let three terms of A.P. are $a - d, a, a + d$
Sum of terms is, $a - d + a + a + d = 33 \Rightarrow a = 11$
Product of terms is, $(a-d)a(a+d) = 11(121 - d^2) = 1155$
$\Rightarrow 121 - d^2 = 105 \Rightarrow d = \pm 4$
$T_{11} = T_1 + 10d = 7 + 10(4) = 47$
if $d = -4$
$T_{11} = T_1 + 10d = 15 + 10(-4) = -25$
BETA
