Question

Determine the AP whose third term is 16 and the 7^th term exceeds the 5^th term by 12.

Answer 1

Given : An A.P in which 

a₃ = a + 2d = 16 …… (1) 

and a₇ = a₅ + 12 i

.e., a + 6d = a + 4d + 12 

⇒ 6d – 4d = 12 

⇒ 2d = 12 

⇒ d = 12/2 = 6 

Substituting d = 6 in equation (1) we get 

a + 2 × 6 = 16 

⇒ a = 16 – 12 = 4 

∴ The series/A.P is 

a, a + d, a + 2d, a + 3d, ……. 

⇒ 4, 4 + 6, 4 + 12, 4 + 18, …… 

⇒ A.P.: 4, 10, 16, 22, …….