After inserting x A.M's. between 2 and 38, the sum of the resulting pr

1.	After inserting x A.M's. between 2 and 38, the sum of the resulting progression is 200. What is the value of x?
Answer» After inserting x A.M's between 2 and 38, we get an A.P. of (x + 2) terms with first term as 2 and last term as 38. Now, sum of n terms of an A.P. = \(\frac{n}{2}\) (a + l), where a = first term, l = last term ∴ Here, 200 = \(\frac{(x+2)}{2}\)(2+38) ⇒ 200 = 20 (x + 2) ⇒ 20x + 40 = 200 ⇒ 20x = 160 ⇒ x = 8

After inserting x A.M's. between 2 and 38, the sum of the resulting progression is 200. What is the value of x?

Answer»

After inserting x A.M's between 2 and 38, we get an A.P. of (x + 2) terms with first term as 2 and last term as 38.

Now, sum of n terms of an A.P. = \(\frac{n}{2}\) (a + l), where a = first term, l = last term

∴ Here, 200 = \(\frac{(x+2)}{2}\)(2+38) ⇒ 200 = 20 (x + 2)

⇒ 20x + 40 = 200

⇒ 20x = 160

⇒ x = 8