Question

Determine the nth term of the AP whose 7^th term is -1 and 16^th term is 17. 

Answer 1

Let a be the first term and d be the common difference of the AP. Then,

a₇ = -1

⇒ a + (7-1) d = -1                  [ a_n  = a + (n-1)d]

⇒ a+ 6d = -1               .................(1)

Also ,

a₁₆  = 17

⇒ a + 15d = 17             .................(2)

from (1)and (2), we get

-1-6d+15d=17

⇒9d = 17 + 1 =18

⇒ d= 2

Putting d = 2 in (1), we get

a+6×2=-1

⇒ a = -1-12=-13

∴ a_n  = a+ (n-1)d

=-13 +(n-1) × 2

=2n -15

Hence, the nth term of the AP is (2n - 15).