Question

the sum of three consecutive numbers is 24 and the sum of their squares is 194.Find the number.

Answer 1

let, the numbers be a-d,a,a+d

By given condition (a-d)+a+(a+b)=24

or 3a = 24

.°. a = 8

By second given condition

(a-d)²+a²+(a+d)²= 224

= (8-d)²+8²+(8+d)²=224

= 2(64+d²)= 224-64=160

=64+d=80=> d² = 16, d = ±4

.-. the required numbers are a-d,a,a+for 4,8,12