Question

If the sum of three numbers which are in A.P is 27 and the product of first and last is 77, then the numbers are

• A. $7,9,11$
• B. $6,9,123$
• C. $7,10,11$
• D. None

Answer 1

The correct option is A $7,9,11$

Let the numbers be $a_1-d,a_1,a_1+d$

Hence their sum is

$(a_1-d)+\left(a_1\right)+(a_1+d)=27$

$3a_1=27$

$a_1=9$

Now

First term is $9-d$ and the last term is $(9+d)$.

Hence their product is

$(9-d)(9+d)=77$

$81-d^2=77$

$81-77=d^2$

$d^2=4$

$d=2$.

Hence the numbers are

$9-2,9,9+2$
$=7,9,11$.