Question

An ap consists of thirty seven terms the sum of middle most terms are to twenty five and the sum of last three terms is four twenty nine find the ap

Answer 1

An ERROR:

Que. An A.P. Consist of 37 Terms. The Sum of Three middle most term is 225 and the sum of the last three term is 429. Find the A.P.

Solution:-

Given:-

☆ A.P. Consist of 37 Terms.

☆ Sum of Three Middle Most Term = 225.

☆ Sum of Last three terms = 429.

Now,

Middle Term for an ODD A.P = (37 + 1)/2

=> Middle most Term = 19.

Hence,

Three Middle Most Term = 18, 19 & 20.

A.T.Q.

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

=> 3a + 54d = 225

=> a + 18d = 75

=> a = 75 - 18d______________(1).

Sum of Last Three Term,

=> ( a +37d ) + ( a+36d) + (a+35d) = 429

=> 3a + 108d = 429

=> a + 36d = 143__________(2)

Putting eq(1) in eq(2). we get,

=> 75 - 18d + 36d = 143

=> 17d = 143 - 75

=> d = 68/17

=> d = 4

Now,

Substituting d=4 in eq(1).

=> a = 75 - 18×4

=> a = 75 - 72

=> a = 3.

Hence,

The A.P. is 3, 7, 11, 15,.........