Question

Sum of first three terms in anathematic progression is 24 and the sum of square is 224 find first three terms of the arthamatic progression

Answer 1

Sum of first three terms in anathematic progression is 24 and the sum of square is 224 find first three terms of the arthamatic progression.

Answer-

Let the three terms of an A.P are
(a+d), a, (a-d).

a+d+a+a-d = 24

3a = 24

a = 24/3

a = 8............. (1 )

And,

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

a^2+d^2+2ad+a^2+a^2+d^2-2ad=224

3a^2+2b^2 = 224............( 2 )

from equation 1 put the value of a in equation 2 ,we get

3 × 8^2 +2d^2 = 224

3 × 64+2d^2 = 224

192 + 2d^2 = 224

2d^2 = 224-192

2d^2= 32

d^2 = 32/2

ď^2 = 16

d = +_4

First three terms of an A. P are

a+d = 8+4 = 12

a = 8

a-d = 8-4 = 4

Or

a+d = 8-4 = 4

a = 8

a-d =8-(-4)= 12