Question

An AP consist of 37 terms.The sum of the three middle most terms is 225 and the sum of the last three terms is 429.Find its AP.

Answer 1

Hey as I think ap is 3,7,11,15
is this correct answe pls comment fast

Answer 2

HEY MATE HERE IS YOUR ANS.

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Let the first term =a and the common difference =d of the A.P.

Since the A.P contains 37 terms.

.°. 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 …

 

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HOPE IT HELPS YOU MATE...

BY GURVEER..

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