Question

The sum of three numbers in A.P. is 15 whereas sum of their squares is 83. Find the smallest of those three numbers.

Answer 1

Let the three numbers in A.P. be $a-d,a,a+d$ Sum$=3a=15$

$a=5$ Sum of their squares$={(a-d)}^2+a^2+{(a+d)}^2=83$

$3a^2+2d^2=83$

$2d^2=83-3\times 25$

$d^2=4$ or $d=\pm 2$

Hence the numbers are $3,5,7$ or $7,5,3$