   # 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?

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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? posted Jan 30, 2018

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}. answer Jan 31, 2018

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