The given Arithmetic Progression (A.P.) is \(3, 8, 13, 18, ….\).
For this A.P., the first term is \(a = 3\) and the common difference is \(d = a_2 − a_1 = 8 − 3 = 5\).
Let the nth term of this A.P. be 78.
The formula for the nth term of an A.P. is \(a_n = a + (n − 1) d \).
Substituting the given values: \(78 = 3 + (n − 1) 5\).
Subtracting 3 from both sides: \(75 = (n − 1) 5\).
Dividing both sides by 5: \((n − 1) = 15\).
Adding 1 to both sides: \(n = 16\).
Therefore, the \(16^{th}\) term of this A.P. is 78.