Question

The sum of first three terms of an

a.p is 24 and the sum of their squares is 224. find the first three terms of the

a.p

Answer 1

the terms r 4 , 8 and 12

Answer 2

First three terms in ap are

(a+d), a, (a-d)

a+d+a+a-d =24

3a =24

a =24/3

a =8

Now,

(a+d)²+a²+(a-d)² =224

___________,

By formula (a+b)²=a²+b²+2ab

Or

(a-b)²=a²+b²-2ab
_____________,,,,

a²+d²+2ad +a²+a²+d²-2ad =224

Putting the value of a

8²+2d²+8²+8² =224

64+64+64+2d²=224


192+2d²=224

2d²=224-192

2d²=32

d²=32/2

d²=16

d=√16

d=4


Now,

Terms are :-

(a+d), a, (a-d)

8+4,8,8-4

12,8,4


I hope this will help you


-by ABHAY