Question

If the sum of three consecutive terms of an A.P is $51$ and the product of last and first term is $273$, then the numbers

• A. $21,17,13$
• B. $20,16,12$
• C. $22,18,14$
• D. $24,20,16$

Answer 1

The correct option is A

$21,17,13$

Step 1: Find the $a$.

Let $a-d$, $a$ and $a+d$be the three numbers.

$\begin{array}{rcl}Sum& \Rightarrow & 3a=51\\ a& =& 51/3\\ a& =& 17\end{array}$

Step 2: Find the $d$.

Given the product of last and first term $=273$

$\begin{array}{rcl}(a-d)(a+d)& =& 273\\ a^2-d^2& =& 273\\ 289–d^2& =& 273\\ d^2& =& 16\\ d& =& 4\end{array}$

Therefore, the numbers are $21,17,13.$

Hence, option A is the correct answer.