Which term of the AP : 3, 8, 13, 18, . . . , is 78?

Solution:

Given,

3, 8, 13, 18, …

First term, a = 3

Common difference, d = a₂ − a₁ = 8 − 3 = 5

Let the nth term of the given A.P. be 78.

a_n = a + (n − 1) d

Therefore,

78 = 3 + (n − 1)5

75 = (n − 1)5

(n − 1) = 15

n = 16

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