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

Question

An arithmetic sequence formed of 11 terms, and the sum of all its terms equals to 220. Find the middle term in that sequence.

Answer 1

Generalized term in any AP can be written as a + (n - 1)d where a > Initial term and d > Common Difference
Now its given that a + 36d + a + 35d + a + 34d = 429 ie.,
3a + 105d = 429 ---- 1
Also its given that a + 17d + a + 18d + a +19d = 225 ie.,
3a + 54d = 225 ---- 2
1 - 2
105d - 54d = 429 - 225
51d = 204
d = 4 ---- 3
Sub 3 in 2
3a = 225 - 54x4
3a = 9
a = 3

Therefore the given AP is 3, 7, 11, 15, 19,.........147{37th Term}.