Sequences And Series Ques 56
If the sum and product of the first three terms in an AP are $33$ and $1155$, respectively, then a value of its $11$ th term is
(2019 Main, 9 April II)
(a) $ 25$
(b) $-36$
(c) $-25$
(d) $-35$
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Answer:
Correct Answer: 56.(c)
Solution:
- Let first three terms of an $AP$ as $a-d, a, a+d$.
So, $\quad 3 a=33 \Rightarrow a=11$
[given sum of three terms $=33$ and product of terms $=1155]$
$ \begin{array}{cc} \Rightarrow & (11-d) 11(11+d)=1155 \\ \Rightarrow & 11^{2}-d^{2}=105 \\ \Rightarrow & d^{2}=121-105=16 \\ \Rightarrow & d= \pm 4 \end{array} $
So the first three terms of the AP are either $7, 11, 15$ or $15,11,7$.
So, the $11$ th term is either $7+(10 \times 4)=47$
or $15+(10 \times(-4))=-25$.
BETA
