Find the 8th term from end of the A.P. 7, 10, 13, ..., 184.

Here, a = 7, d = 10 – 7 = 3 and l = 184

where l = a + (n – 1)d

Now, to find the 8^th term from the end, we will find the total number of terms in the AP.

So, 184 = 7 + (n – 1)(3)

⇒ 184 = 7 + 3n – 3

⇒ 184 = 4 + 3n

⇒ 180 = 3n

⇒ n = 60

So, there are 60 terms in the given AP.

Last term = 60^th

Second last term = 60 – 1 = 59^th

Third last term = 60 – 2 = 58^th

And so, on

So, the 8^th term from the end = 60 – 7 = 53^th term

So, a_n = a + (n – 1)d

⇒ a₅₃ = 7 + (53 – 1)(3)

⇒ a₅₃ = 7 + 52 × 3

⇒ a₅₃ = 7 + 156

⇒ a₅₃ = 163