In an A.P., the sum of its first n terms is 6n - n². Find its 25th term.

Given, S_n = 6n - n².

So, sum of (n -1) terms will be

⇒ S_{n - 1} = 6(n - 1) - (n - 1)²
⇒ S_{n - 1} = 6n - 6 -(n² + 1 - 2n)
⇒ S_{n - 1} = 6n - 6 - n² - 1 + 2n
⇒ S_{n - 1} = 8n - n² - 7.

By formula, a_n = S_n - S_{n - 1}
⇒ a_n = 6n - n² - (8n - n² - 7)
⇒ a_n = 6n - 8n - n² + n² + 7
⇒ a_n = -2n + 7.

∴ a₂₅ = -2(25) + 7 = -50 + 7 = -43.

Hence, the 25th term of the A.P. is -43.