Question

The sum of first three term season ap is 24 and the sum of their squares is 224 find the first three terms of this AP

Answer 1

Step-by-step explanation:

The sum of first three terms in an AP is 24 and sum of their square is 224, who can find the first three

Let the roots of A.P .be (a-d) ,a,(a+d)

Now the sum of 1st three terms is 24 that means

a-d+a+a+d=24

3a=24

a=8

we got the value of a=8

Now,

squaring the terms

(a-d)22+(a)2+2+(a-d)22=224

where 2 are square not in multiplication

a2+d2-2ad+a2+a2+d2+2ad=224

3a22+2d22=224

3×8×8+2d2=224

2d2=224–192

2d2=32

d2=16

d=4

Therefore a-d,a,a+d are

8–4,8,8+4

4,8,12 ←This are the values of 1st three 3terms