The sum of the first 14 terms of an A.P. is 1505 and its first term is 10. Find its 25th term.

Given, S₁₄ = 1505 and a = 10.

We know that,

$S$n = \dfrac{n}{2}[2a + (n - 1)d] \\[1em] \therefore S{14} = \dfrac{14}{2}[2 \times 10 + (n - 1)d] \\[1em] \Rightarrow 1505 = 7[20 + (14 - 1)d] \\[1em] \Rightarrow 140 + 91d = 1505 \\[1em] \Rightarrow 91d = 1505 - 140 \\[1em] \Rightarrow d = \dfrac{1365}{91} \\[1em] \Rightarrow d = 15 \\[1em]

By formula, a_n = a + (n - 1)d
⇒ a₂₅ = 10 + 24 × 15
= 10 + 360
= 370.

Hence, the 25th term of the A.P. is 370.