Question

The $6^{th}$ term of an A.P. is 16 and the ${14}^{th}$ term is 32. Determine the ${36}^{th}$ term.

Answer 1

Given that,

a₆ = 16 ; a₁₄ = 32.

To find : a₃₆ = ?

Solution :

a₆ = a + 5d = 16

a₁₄ = a + 13 d = 32

Solving the above equations we get,

a + 5d = 16

-a - 13d = - 32

___________

- 8d = - 16

=> 8d = 16

=> d = 16 / 8 = 2

a + 5d = 16

=> a + 5 ( 2 ) = 16

=> a + 10 = 16

=> a = 16 - 10

=> a = 6

Hence a = 6, d = 2.

a₃₆ = a + 35d

=> a₃₆ = 6 + 35 ( 2 )

=> a₃₆ = 6 + 70

=> a₃₆ = 76.

Hence the 36th term of the AP is 76.