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

We know that,

n^th term of an A.P. is given by,

a_n = a + (n - 1)d

Given,

a = 7

d = 10 - 7 = 3

⇒ a_n = 184

⇒ a_n = 7 + (n - 1)3

⇒ 184 = 7 + (n - 1)3

⇒ 184 - 7 = (n -1)3

⇒ 177 = (n - 1)3

⇒ $\dfrac{177}{3}$ = (n - 1)

⇒ (n - 1) = 59

⇒ n = 59 + 1

⇒ n = 60.

There are 60 terms in the A.P.

The 8th term from end of the A.P. is 53rd (60 - 7) term from the starting.

⇒ a₅₃ = 7 + (53 - 1)3

= 7 + (52)3

= 7 + 156

= 163.

Hence, the 8th term from end of the A.P is 163.