Question

Determine the AP whose 3rd term is 5 and the 7^th term is 9.

Answer 1

a₃ = a + (3 – 1)d = a + 2d = 5 … (1) 

a₇ = a + (7 – 1)d = a + 6d = 9 … (2) 

(1) – (2) ⇒ -4d = -4 ⇒ d = 1. 

Sub, d = 1 in (1), we get 

a + 2(1) = 5 

a = 3 

Hence the required A.P. is 3, 4, 5, 6, 7.