Find the 10^th term from the end of the A.P. 4, 9, 14, ……., 254.

We know that r^th term from the end is (n - r + 1)^th term from the beginning, where n is no. of terms.

Let the A.P. 4, 9, 14, ……., 254 has n terms.

The above A.P. has common difference = 9 - 4 = 5 and first term = 4.

Substituting values in a_n = a + (n - 1)d,

⇒ 254 = 4 + (n - 1)5

⇒ 254 = 4 + 5n - 5

⇒ 254 = 5n - 1

⇒ 255 = 5n

⇒ n = 51.

So, 10^th term from the end = (51 - 10 + 1)^th = 42^nd term from beginning.

Substituting values in a_n = a + (n - 1)d,

⇒ a_n = 4 + (42 - 1)5

= 4 + 41(5)

= 4 + 205

= 209.

Hence, 10^th term from the end = 209.