Question

An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three terms is 429. Find the AP.
I need the solution pic.....

Answer 1

$a18 + a19 + a20 = 225 \\ a + 17d + a + 18d + a + 19d = 225 \\ 3a + 54d = 225 \\ a + 18d = 75 ...........(1)\\ a + 34d + a + 35d + a + 36d = 429 \\ 3a + 105d = 429 \\ a + 35d = 143............(2) \\solving \: (1)and(2) \: \: \: \: 17d = 68 \\ d = 4 \\ a = 75 - 18 \times 4 = 75 - 72 = 3 \\ ap \: is \: 3 \: \: \: \: 7 \: \: \: \: 11.......$

Answer 2

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 + 2d,......a + 18d

Sum of 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) = 3

Hence, The AP is 3, 7, 11, ..., 147.