Question

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

Answer 1

\(3, 8, 13, 18, ….\)
For this A.P., \(a = 3\) and \(d = a_2 − a_1 = 8 − 3 = 5\)
Let nth term of this A.P. be 78.
\(a_n = a + (n − 1) d \)
\(78 = 3 + (n − 1) 5\)
\(75 = (n − 1) 5\)
\((n − 1) = 15\)
\(n = 16\)

Hence, \(16^{th}\) term of this A.P. is 78.