or
or
Which number will continue the following series? 3,8,15,24,35,48,63,80___
3 8 15 24 35 48 63 80 99
\ / \ / \ / \ / \ / \ / \ / \ /
+ 5 7 9 11 13 15 17 19
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 \(99\).
