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

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

Now, t₆ = 16  ...(Given)

`\implies` a + 5d = 16   ...(i)

And t₁₄ = 32  ...(Given)

`\implies` a + 13d = 32   ...(ii)

Subtracting (i) from (ii), we get

8d = 16

`\implies` d = 2

`\implies` a + 5(2) = 16

`\implies` a = 6

Hence, 36^th term = t₃₆ 

= a + 35d

= 6 + 35(2)

= 76