What is the next number in the sequence {1, 3, 6, 10, 15, ...}?
Understand the Problem
The question asks for the next number in the sequence {1, 3, 6, 10, 15, ...}. It requires identifying a pattern to derive the next term.
Answer
$21$
Answer for screen readers
The next number in the sequence is $21$.
Steps to Solve
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Identify the Pattern
The sequence given is {1, 3, 6, 10, 15, ...}. Let's notice how each number is formed:
- The first number is 1.
- The second number is 1 + 2 = 3.
- The third number is 3 + 3 = 6.
- The fourth number is 6 + 4 = 10.
- The fifth number is 10 + 5 = 15.
Each term is generated by adding consecutive integers starting from 1.
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Add the Next Integer
Following this pattern, the next term would be obtained by adding 6 (the next consecutive integer) to the last term (15):
$$ 15 + 6 = 21 $$
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Conclusion
Therefore, the next number in the sequence is 21.
The next number in the sequence is $21$.
More Information
This sequence is known as the triangular numbers, where each term represents a triangle's dot arrangement. The $n$-th triangular number can be calculated using the formula $\frac{n(n + 1)}{2}$.
Tips
Common mistakes include:
- Not recognizing the pattern of adding consecutive integers.
- Confusing the sequence with a different arithmetic or geometric progression.
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