Question

the sum of first three terms of an AP is 24 and the sum of the squares is 224. find the AP

Answer 1

consider those terms to be
a-d,a,a+d

their sum= 3a=24(given)

gives us a=8

sum of their squares

(a-d)^2 + a^2 + (a+d)^2 =224

gives us

3a^2 + 2d^2 =224
(and since a=8)

2d^2 = 224-192

2d^2 =32

gives us d =+4,-4

so there can be 2 AP's

1.taking +4 as common difference!

4,8,12........

2.taking -4 as common difference!

12,8,4,...........



hope it helps!

Answer 2

4,8,12 are the term of Ap