Question

Find three numbers in A.P . whose sum is 21 and their product is 231.

Answer 1

Let the $AP$ is $(a-d),a,(a+d)$

$(a-d),a,(a+d)$ $=21$

$3a=21$

$a=7$

$(a-d)\times a\times (a+d)=231$

$\left(a\times a-d\times d\right)\times a=231$

$\left(7\times 7-d\times d\right)\times 7=231$

$\left(7\times 7-d\times d\right)=\frac{231}{7}$

$\left(7\times 7-d\times d\right)=33$

$d\times d=49-33$

$d\times d=16$

$d=4$

Hence, the $A.P$ is $3,7,11$