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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?

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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 by anonymous

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1 Answer

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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 by Tejas Naik



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