Question

i am a bit confused with ap pls help

Answer 1

Heya !!

Let the three middle most terms of the AP be a-d, a, a+d.

We have,
(a-d) + a + (a+d) = 225
=> 3a = 225
=> a = 225/3
=> a = 75

Now, the AP is
a-18d,…, a-2d, a-d, a, a+d, a+2d,..., a+18d

Sum of the last three terms :
(a+18d) + (a+17d) + (a+16d) = 429
=> 3a + 51d = 429
=> a + 17d = 143
=> 75 + 17d = 143
=> 17d = 143 - 75
=> 17d = 68
=> d = 68/17
=> d = 4

Now, first term = a - 18d
=> 75 - 18(4)
=> 75 - 72
=> 3

Therefore, the AP is 3, 7, 11, ..., 147.