Question

help needed
the sum of 3 numbers in AP is 12 and sum of their squares is 56.Find the number 2,4,6.​

Answer 1

AP series :- a,a+d,a+2d,.....

a+a+d+a+2d = 12

3a+3d=12

a+d=4

=>> 2nd term =4

a^2 + (a+d)^2 + (a+2d)^2 =56

a^2 + 4^2 + a^2 +2ad + 4d^2 =56

2a^2 + 16 + 2ad +4d^2 =56

2a^2 + 2ad +4d^2 = 40

a^2 + ad + 2d^2 = 20

a^2 -ad +2ad +2d^2 =20

a(a-d) +2d(a+d) = 20

a-d = 20 or ---(1)

a+2d =20 or

a+d = 20 -----(2)

From (1) and (2)

(1) + (2) = 2a =40

=>> a = 20

a+d = 4

=>> 20 + d = 4

=>> d= -16

Therefore AP series is 20,4,-12