What is the next number in the following series 2, 3, 6, 7, 10, 11?
Understand the Problem
The question is asking us to identify the next number in a given sequence. To approach this, we need to analyze the pattern in the series provided: 2, 3, 6, 7, 10, 11.
Answer
$14$
Answer for screen readers
The next number in the sequence is $14$.
Steps to Solve
- Identify Patterns in the Sequence
Look at the sequence: 2, 3, 6, 7, 10, 11. We need to find a recurring pattern.
- Separate Odd and Even Index Values
Notice the position of the numbers:
- Even indices: 2 (1st), 6 (3rd), 10 (5th)
- Odd indices: 3 (2nd), 7 (4th), 11 (6th)
- Analyze Even Indexed Numbers
The even indexed numbers (2, 6, 10) increase by 4:
- $6 - 2 = 4$
- $10 - 6 = 4$
Continuing this pattern, the next even indexed number would be: $$10 + 4 = 14$$
- Analyze Odd Indexed Numbers
The odd indexed numbers (3, 7, 11) also increase by 4:
- $7 - 3 = 4$
- $11 - 7 = 4$
This pattern suggests that the next odd indexed number would be: $$11 + 4 = 15$$
- Combine Findings for Next Number
The full sequence alternates between the two patterns, so after 11 (the last number given), the next number in the series will be the next even indexed number: $$14$$
The next number in the sequence is $14$.
More Information
In this sequence, we see a clear pattern where both the even and odd indexed numbers increase by 4. This means that through the patterns identified, we can confidently determine subsequent values.
Tips
- Focusing only on one part of the sequence and not recognizing the alternating patterns can lead to errors.
- Skipping the step of verifying the increment size may result in choosing incorrect numbers.
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