Answer :
To find the missing number in the sequence 6, 5, 8, 13, 10, 21, 12, 29, 14, ?, we need to look for a pattern in the numbers provided.
Let's break down the sequence step-by-step:
- Start with 6, then it decreases by 1 to become 5.
- Next, it increases by 3 to become 8.
- Then, it increases by 5 to become 13.
- It decreases by 3 to become 10.
- Increases by 11 to become 21.
- Decreases by 11 to become 12.
- Increases by 17 to become 29.
- Decreases by 15 to become 14.
If we observe the pattern of increases and decreases:
- The increases appear to be prime numbers: 3, 5, 11, 17
- The decreases are increasing odd numbers: 1, 3, 11, 15
To find the next number:
- Since the last change was a decrease (by 15), the next should be an increase. Following the sequence of prime numbers used for increases, the next prime number after 17 is 19.
So, add 19 to 14:
[tex]14 + 19 = 33[/tex]
Therefore, the next number in the sequence is 33.
