The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.

Given, a = 15, S₁₅ = 750

By formula, S_n = $\dfrac{n}{2}[2a + (n - 1)d]$

$\Rightarrow S_{15} = \dfrac{15}{2}[2 \times 15 + (15 - 1)d] \\[1em] \Rightarrow 750 = \dfrac{15}{2}[30 + 14d] \\[1em] \Rightarrow 750 \times 2 = 450 + 210d \\[1em] \Rightarrow 450 + 210d = 1500 \\[1em] \Rightarrow 210d = 1500 - 450 \\[1em] \Rightarrow 210d = 1050 \\[1em] \Rightarrow d = \dfrac{1050}{210} \\[1em] \Rightarrow d = 5.$

By formula, a_n = a + (n - 1)d
⇒ a₂₀ = 15 + (20 - 1)5
⇒ a₂₀ = 15 + 95
⇒ a₂₀ = 110.

Hence, the 20th term of the A.P. is 110.