Question

plz ans give in english.

Answer 1

Let the Numbers are

a-3d , a-d , a+d , a+3d

ATQ,

a-3d+a-d+a+d+a+3d = 32

=> 4a = 32 => a = 8

And,

(a-3d)(a+3d) : (a-d)(a+d) = 7:15

=> a²-9d²/a²-d² = 7/15

=> 8²-9d²/8²-d² = 7/15

=> 64×15-9d²×15 = 64×7-7d²

=> 64(15-7) = 135d²-7d²

=> 64×8 = 128d²

d² = 4

=> d = ± 2

Hence The number are

8,10,12,14

Answer 2

Let the Numbers are
a-3d , a-d , a+d , a+3d
according to question
a-3d+a-d+a+d+a+3d = 32
= 4 a = 32
= a = 8
And,
(a-3 d)(a+3 d) : (a-d) (a+d) = 7:15
= a²-9 d²/ a²- d² = 7/15
= 8²-9d²/8²-d² = 7/15
= 64×15-9d²×15 = 64×7-7d²
= 64(15-7) = 135d²-7d²
= 64×8 = 128d²
d² = 4
= d = ± 2
Hence The number are
a, a+d, a+2d, a+3d
8,10,12,14