Question

Determine the general term of an A.P. whose 7^th term is –1 and 16^th term 17

Answer 1

Let a be the first term and d be the common difference of the given A.P. Let the A.P. be a1, a₂ , a₃ , ……. a_n , …….

It is given that a₇ = – 1 and a₁₆ = 17

a + (7 – 1) d = – 1 and, a + (16 – 1) d = 17

⇒ a + 6d = – 1 ….(i) and, a + 15d = 17 ….(ii)

Subtracting equation (i) from equation (ii), we get

9d = 18 ⇒ d = 2

Putting d = 2 in equation (i), we get

a + 12 = – 1 ⇒ a = – 13

Now, General term = an

= a + (n – 1) d = – 13 + (n – 1) × 2 = 2n – 15