Question

the sum of the three middle most term is 225 and the sum of the last 3 terms is 429 find the AP

Answer 1

____________________________________________________________

Hey mate !!

Here's your answer !!

Let the first term and the common difference of the A.P are ' a ' and ' d ' respectively.

Since the A.P contains 37 terms. So, the middle most term is:

 (37+1)/2 th term = 19th term.

Thus, three middle most terms of this A.P.are 18th, 19th and 20th terms.

Given a 18 + a 19 + a 20 = 225

⇒ (a + 17d) + (a + 18d) + (a + 19d) = 225

⇒ 3(a + 18d) = 225

⇒ a + 18d = 75

⇒ a = 75 – 18d … (1) 

According to given information,

a 35 + a 36 + a 37 = 429

⇒ (a + 34d) + (a + 35d) + (a + 36d) = 429

⇒ 3(a + 35d) = 429

⇒ (75 – 18d) + 35d = 143

⇒ 17d = 143 – 75 = 68

⇒ d = 4 

Substituting the value of d in equation (1), it is obtained

a = 75 – 18 × 4 = 3 

Thus, the A.P. is 3, 7, 11, 15 … 

Hope this helps you !!

Cheers !!
____________________________________________________________

# Kalpesh :)