Find:

nth term of the A.P. 13, 8, 3, -2,……

A.P is known for Arithmetic Progression whose common difference = a_n – a_n-1 where n > 0

a = a₁ = 13, a₂ = 8

Common difference, d = a₂ – a₁ = 8 – 13 = -5

We know, a_n = a + (n-1) d where a is first term or a₁ and d is common difference

∴ a_n = 13 + (n-1) -5

⇒ a_n = 13 – 5n + 5

⇒ a_n = 18 – 5n

Hence, n^th term of A.P. is 18 – 5n