Question

Find the seventeenth term from the end of the AP 1,6,11....216

Answer 1

According to the question :-

First term = a = 1

Second term = a + d = 6

Common Difference = a + d - a  = d = 6 - 1 = 5

Now, let 216 be the last term( or nth term ) of the given AS.

∴ 216 = a + ( n - 1 )d

⇒ 216 = 1 + ( n - 1 )5

⇒ 216 - 1 =  ( n -1 )5

⇒ 215 / 5 = n - 1

⇒ 43 = n - 1

⇒ 43 + 1 = n

⇒ 44 = n

Therefore, 216 is the 44th term of the given AS.

17 th term from the end = 44 terms - 16 terms = 28 terms

23rd term = a + ( 28 - 1 )d

             ⇒ 1 + ( 27 )5

             ⇒ 1 + 135

             ⇒ 136

Therefore, 136 is the seventeenth term from the end of the AP 1, 6 , 11 .... 216.

Answer 2

REFER THE ATTACHMENT.