Question

An



a. P consist of 37 term the sum of 3 middle most term is 225 and the last 3 trm is 429 find the ap

Answer 1

Let the first term be a and the common difference be d.
Now it is given that n = 37....so middle most term = n+1/2 = 37 + 1/2 =38/2 = 19.
so middle most term is a19
Now, a18 + a19 + a20 = 225
i.e. 3a + 54d = 225
i.e. a + 18d = 75.....(1)
also, a35 + a36 + a37 = 429
or,. a+34d +a+35d+a+36d = 429
or,. 3a + 105d = 429
or,. a + 35d = 143......(2)
Now subtracting (1) from (2) we get
17d = 68 i.e. d = 4.
Now putting d=4 in (1) we get,
a + 18×4 = 75
a = 75-72 i.e a = 3
So the a.p. is 3,7,11,15,19..