If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is :
A. 13 B. 9 C. 21 D. 17Answer: Option CShow Answer
Solution(By Apex Team)
Let three consecutive terms of an increasing A.P. be a – d, a + d
where a is the first term and d be the common difference
$\begin{aligned}&\therefore a-d+a+a+d=51\\
&\Rightarrow3a+51\\
&\therefore a=\frac{51}{3}=17\end{aligned}$
and product of the first and third terms
$\begin{array}{l}=(a-d)(a+d)=273\\
\Rightarrow a^2-d^2=273\\
\Rightarrow(17)^2-d^2=273\\
\Rightarrow289-d^2=273\\
\Rightarrow d^2=289-273\\
\Rightarrow d^2=16\\
\Rightarrow d^2=(\pm4)^2\\
\therefore d=\pm4\\
\because\text{ The A.P. is increasing }\\
\therefore d=4\\
\text{ Now third term }=a+d\\
=17+4=21\end{array}$
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