Which number will continue the following series? 3,8,15,24,35,48,63,80___

To determine the next number in the series \(3, 8, 15, 24, 35, 48, 63, 80\), let's analyze the pattern.

Observing the Pattern:
1. Calculate the differences between consecutive terms:
  - \(8 - 3 = 5\)
  - \(15 - 8 = 7\)
  - \(24 - 15 = 9\)
  - \(35 - 24 = 11\)
  - \(48 - 35 = 13\)
  - \(63 - 48 = 15\)
  - \(80 - 63 = 17\)

  The differences are: \(5, 7, 9, 11, 13, 15, 17\)

2. Notice that these differences form an arithmetic sequence with a common difference of 2.

Predicting the Next Term:
- The last difference in the sequence is 17.
- Following the pattern, the next difference should be \(17 + 2 = 19\).

- Add this difference to the last term in the original series:
 \[
 80 + 19 = 99
 \]

Therefore, the next number in the series is \(99\).

3     8     15   24   35    48    63    80   99
\    /  \    /  \   /  \   /  \   /  \   /  \    /  \    /
  + 5     7     9      11   13   15    17     19