If the sum and product of the first three terms in an A.P.
Question:

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

1. (1) $-35$

2. (2) 25

3. (3) $-36$

4. (4) $-25$

Correct Option: , 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 bf terms is, $(a-d) a(a+d)=11\left(121-d^{2}\right)=1155$

$\Rightarrow 121-d^{2}=105 \Rightarrow d=\pm 4$

if $d=4$

$\mathrm{T}_{11}=\mathrm{T}_{1}+10 d=7+10(4)=47$

if $d=-4$

$\mathrm{T}_{11}=\mathrm{T}_{1}+10 d=15+10(-4)=-25$