Sum of the first 14 terms of an AP is 1505 and its first term is 10. Find its 25th term.

Here, first term = a = 10

Let the Common difference = d

Sum of first 14 terms = S₁₄ = 1505

Now, Sum of n terms of this arithmetic series is given by:

S_n = [2a + (n - 1)d]

∴ S₁₄ = [2(10) + (14 - 1)d] = 1505

⇒ 7 × [20 + 13d] = 1505

⇒ [20 + 13d] = 215

⇒ 13d = 195

⇒ d = 15

Now, n^th term is given by:

∴ a_n = a + (n - 1)d

⇒ a₂₅ = 10 + (25 - 1)15

= 10 + (24 × 15)

= 10 + 360

= 370