Question

the sum of four numbers which are in ap is 120 then fine the value of a​

Answer 1

A N S W E R :

Let the numbers be (a – 3d), (a ­– d), (a + d), (a + 3d),

Then,

 Sum = 20

 (a – 3d) + (a – d) + (a + d) + (a + 3d) = 20

 4a = 20           

 a = 5

 Sum of the squares = 120

(a−3d)2   + (a−d)2 + (a+d)2 + (a+3d)2 = 120

4a2 + 20d2 = 120

a2 + 5 d2 = 30

25 + 5d2 = 30                   [Since, a = 5]

5d2 = 5           

d = ± 1           

If d = 1, then the numbers are 2, 4, 6, 8. If d = – 1, then the numbers are 8, 6, 4, 2.

Thus, the numbers are 2, 4, 6, 8 or 8, 6, 4, 2.