If the 5^th and 11^th terms of an A.P. are 16 and 34 respectively. Find the A.P.

Let first term be a and common difference be d of A.P.

By formula,

⇒ a_n = a + (n - 1)d

5^th term = 16

⇒ a₅ = 16

⇒ a + (5 - 1)d = 16

⇒ a + 4d = 16 ………(1)

11^th term = 34

⇒ a₁₁ = 34

⇒ a + (11 - 1)d = 34

⇒ a + 10d = 34 ……..(2)

Subtracting equation (1) from (2), we get :

⇒ a + 10d - (a + 4d) = 34 - 16

⇒ a - a + 10d - 4d = 18

⇒ 6d = 18

⇒ d = 3.

Substituting value of d in equation (1), we get :

⇒ a + 4(3) = 16

⇒ a + 12 = 16

⇒ a = 4.

A.P. = a, (a + d), (a + 2d), ……..

= 4, (4 + 3), (4 + 2 × 3), ……..

= 4, 7, 10, …….

Hence, A.P. = 4, 7, 10, …….