1.

An A.P consist of 37 terms. the sum of three middle most term is 225 and the sum of last 3 term is 429. find AP?

Answer»

The middlemost term is (37 + 1) /2 = 19.
Therefore
The THREE middle most TERMS are a18 , a19 and a20.
=> a18 + a19 + a20 = 225.
=> a + 17d + a + 18d + a + 19d = 225
=> 3a + 54d = 225
=> a + 18d = 75 ---------eq.1


Last three terms are a35 , a36 and a37.
Therefore
a + 34d + a + 35d + a + 36d = 429.
=> 3a + 105d = 429
=> a + 35d = 143 ----------eq.2


Solving EQUATIONS 1 and 2
We get
a = 3
d = 4

The AP is 3,7,11,15.........


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