Question

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

Answer 1

ur three middle most terms would be 18th term 19th term and 20th term...and ur last three terms would be 35th 36th and 37th term..now u can solve the prblm as follows..
AP: 3, 7, 11....

Answer 2

let the three middlemost term be a-d , a , a+d
 
a-d+a+a+d =3a = 225
a = 225/3
Here a is the middle term
From a the last term is 18th
so a+18d is the last term
Sum of last three term = a+18d + a+17d + a+16d = 429
 3a + 51d = 429
225 + 51d = 429
51d = 429 - 225 = 204
d = 204/51 = 4

The first term of AP is a-18d because middle term is a
a-18d = 75 - 18×4 = 75 - 72 =3
 second term = a-17d = 75 - 17 × 4 = 75 - 68 = 7
Last term is a + 18d = 75 +72 = 147

So the AP is 3,7, ....... 147