Question

The 16th and 17th term of an A.P. are 19 and 41. Find 40th term

Answer 1

Given, the 6th and 17th term of an A.P. are 19 and 41 respectively.

⇒ a6 = a + (6 -1)d = 19

⇒ a + 5d = 19 ... (1)

Also, a17 = a + (17 -1)d = 41

⇒ a + 16d = 41 ... (2)

On subtracting (1) from (2), we get

a + 16d - (a + 5d) = 41 - 19

⇒ 11d = 22

⇒ d = 2

On putting d = 2 in (1), we get

a + 5(2) = 19

⇒ a = 9

Now, 40th term of the a.p. is:

a40 = a + (40 -1)d = a + 39d

= 9 + 39(2) = 9 + 78 = 87