Question

An ap starts from 50. if the ratio of 4th and 7th term is 28:31. find the common difference and S20

Answer 1

Solution :

Given that, the first term of an AP is 50

Let us consider that the common difference is d

So, we get the AP as

50, 50 + d, 50 + 2d, ...

The 4th term be (50 + 3d) and the 7th term be (50 + 6d).

ATQ, (50 + 3d) : (50 + 6d) = 28 : 31

⇒ (50 + 3d) / (50 + 6d) = 28 / 31

⇒ 31 (50 + 3d) = 28 (50 + 6d)

⇒ 1550 + 93d = 1400 + 168d

⇒ 168d - 93d = 1550 - 1400

⇒ 75d = 150

⇒ d = 2

∴ the common difference is 2.

Now, S₂₀

= 20/2 * [ (2 * 50) + {(20 - 1) * 2} ]

= 10 * (100 + 38)

= 10 * 138

= 1380