Question

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. $17$

Answer 1

The correct option is C $21$

Let the three terms in A.P. be $a-d,a,a+d$.

Sum of the three terms = $3a$ = $51$

$\Rightarrow$ $a=17$

Product of first and third term is $(a-d)(a+d)$

$\Rightarrow$ $a^2-d^2=273$

$\Rightarrow$ $289-d^2=273$

$\Rightarrow$ $d^2=16$

$d$ takes positive value as it is an increasing A.P.

$\Rightarrow$ $d=4$

$\Rightarrow$ Third term = $a+d=17+4=21$

$\Rightarrow$ Third term = $21$

$\therefore$ Option C is correct.