Question

If the sum and product of the first three terms in an $A.P.$ are $33$ and $1155$, respectively, then the value of its ${11}^{\text{th}}$ term is :

• A. $-36$
• B. $-25$
• C. $25$
• D. $-35$

Answer 1

The correct option is B $-25$

Let the terms of $A.P.$ are $a-d,a,a+d$.
$\therefore$ Sum $=33\Rightarrow a-d+a+a+d=33$

$3a=33$
or, $a=11$

Given, Product $=1155$

$\therefore (a-d)\times a\times (a+d)=1155$
$\Rightarrow (11-d)\times 11\times (11+d)=1155$
$\Rightarrow 121-d^2=105\Rightarrow d=\pm 4$

If $d=4$,
First term, $a-d=7$

$\because a_n=a+(n-1)d$
$\because$ $a_{11}=a-d+10d=47$ (replacing $a=a-d$ in the formula)

If $d=-4$,
First term, $a-d=15$
$a_{11}=a-d+10d=-25$

$\therefore$ Value of 11th term from the given options is -25.