The 3^rd and 8^th term of an arithmetic progression are -13 and 2 respectively. What is the 14^th term?

Let the first term of an AP = a and the common difference = d
3^rd term of AP = A₃ = a + 2d = -13 ...... (1)
8^th term = A₈ = a + 7d = 2 ...... (2)
Subtracting equation (1) from (2), we get :
⇒ 7d - 2d = 2 - (-13)
⇒ 5d = 15
⇒ d = $$\frac{{15}}{5}$$ = 3
Substituting it in equation (2)
⇒ a = 2 - 7(3) = 2 - 21 = -19
∴ 14^th term = A₁₄ = a + 13d
= -19 + 13(3)
= -19 + 39
= 20