Which term of the A.P. $3, 8, 13, 18, \dots$is $78$ ?

Given the A.P. series as 3, 8, 13, 18, …

The first term, a₁ = 3

Common difference, d = a₂ − a₁ 

                                   = 8 − 3 

                                   = 5

Let the n^th term of the given A.P. be 78. 

Now as we know,

a_n = a + (n−1)d

By substituting the values we get,

78 = 3 + (n −1)5

⇒ 75 = (n−1)5           

⇒ (n−1) = 15

⇒ n = 16

Hence,  the 16^th term of this A.P. is 78.