Which of the following numbers will replace the question mark (?) in the given series?
78, 86, 258, 322, ?

The correct option is 1610.

To find the missing number in the series, let us analyze the pattern of operations between consecutive terms:
The given series is: 78, 86, 258, 322, ?

Let us look at the transition from the first term to the second term:
78 to 86 involves adding 8, which can be written as 8 raised to the power of 1:
$78+8^1=78+8=86$

Now, let us look at the transition from the second term to the third term:
86 to 258 involves multiplying by 3:
$86\times 3=258$

Next, look at the transition from the third term to the fourth term:
258 to 322 involves adding 64, which is 8 raised to the power of 2:
$258+8^2=258+64=322$

Following this alternating pattern of operations (adding powers of 8, then multiplying by consecutive odd numbers 3, 5, etc.):
The next operation to find the fifth term must be to multiply the fourth term by 5:
$322\times 5=1610$

Thus, the number that replaces the question mark in the series is 1610.