Let’s consider the four terms of the A.P. to be (a – 3d), (a – d), (a + d) and (a + 3d).
From the question,
Sum of these terms = 50
⇒ (a – 3d) + (a – d) + (a + d) + (a + 3d) = 50
⇒ a – 3d + a – d + a + d + a – 3d= 50
⇒ 4a = 50
⇒ a = 50/4 = 25/2
And, also given that the greatest number = 4 x least number
⇒ a + 3d = 4 (a – 3d)
⇒ a + 3d = 4a – 12d
⇒ 4a – a = 3d + 12d
⇒3a = 15d
⇒a = 5d
Using the value of a in the above equation, we have
⇒25/2 = 5d
⇒ d = 5/2
So, the terms will be:
(a – 3d) = (25/2 – 3(5/2)), (a – d) = (25/2 – 5/2), (25/2 + 5/2) and (25/2 + 3(5/2)).
⇒ 5, 10, 15, 20