To understand and find the missing number in the series, follow the detailed explanation below:
Given series: 1, 3, 6, 5, 7, 10, 11, 13, 16, 21, 24
We need to determine the pattern within the series to find the missing number.
Let's evaluate the series by looking closely at the terms and their positions:
1. The first term is 1.
2. The second term is 3.
3. The third term is 6.
4. The fourth term is 5.
From this, we might observe an alternating pattern where the terms either increase by an increment or repeat a pattern.
Start differentiating the terms at odd and even indices to see if a pattern emerges:
- 1st term: 1
- 3rd term: 6
- 5th term: 7
- 7th term: 11
- 9th term: 16
Now looking at another subset:
- 2nd term: 3
- 4th term: 5
- 6th term: 10
- 8th term: 13
- 10th term: 21
This suggests an alternating pattern where odd indices and even indices may have separate sequences.
Analyzing odd indices:
1, 6, 7, 11, 16:
- 6 - 1 = 5 (increment)
- 7 - 6 = 1 (small increment)
- 11 - 7 = 4 (increment)
- 16 - 11 = 5 (increment)
Odd indices seem to somewhat follow a pattern of increasing alternately.
Analyzing even indices:
3, 5, 10, 13, 21:
- 5 - 3 = 2 (increment)
- 10 - 5 = 5 (increment)
- 13 - 10 = 3 (increment)
- 21 - 13 = 8 (increment)
Let's now identify the pattern before and after the missing number:
Before the missing number, we have 16; after, we have 21.
Contextually, we can infer the pattern in a simpler linear progression. Hence:
- Each subset pattern influences the incremental steps.
Thus, observing the pattern closely and understanding the incremental steps between terms allows us to determine the missing number is 16.
Therefore, the missing number in the series 1, 3, 6, 5, 7, 10, 11, 13, 16, 21, 24 is 16.
