An ap consist of 37 terms. The sum of the three middle most termsis 225 and the sum of the last three terms is429. Find the ap
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The AP has 37 terms.
The middle term is the 19th term.
So the sum of the middle three terms = (a+17d)+(a+18d)+(a+19) = 225, or
3a + 54d = 225, or
a+18d = 75 …(1)
So the sum of the last three terms = (a+34d)+(a+35d)+(a+36) = 429, or
3a+105 = 429, or
a + 35d = 143 …(2)
Subtract (1) from (2)
17d = 143–75 = 68, or d = 68/17 = 4.
From (1), a = 75–18d = 75–72 = 3.
The middle term is the 19th term.
So the sum of the middle three terms = (a+17d)+(a+18d)+(a+19) = 225, or
3a + 54d = 225, or
a+18d = 75 …(1)
So the sum of the last three terms = (a+34d)+(a+35d)+(a+36) = 429, or
3a+105 = 429, or
a + 35d = 143 …(2)
Subtract (1) from (2)
17d = 143–75 = 68, or d = 68/17 = 4.
From (1), a = 75–18d = 75–72 = 3.
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