Tell me if Digits are in Sequence like 1,3,8,21,55 then what will be the next digit

The given sequence is: 1, 3, 8, 21, 55.

This is not a simple arithmetic or geometric sequence, but rather it resembles a pattern often seen in recursive or complex sequences. After careful examination, it appears to be a variation of the Fibonacci sequence where each term is generated based on a relationship involving the previous terms.

Let's break it down:

1. **1 to 3**: The difference is 2.
2. **3 to 8**: The difference is 5.
3. **8 to 21**: The difference is 13.
4. **21 to 55**: The difference is 34.

Notice that the differences (2, 5, 13, 34) are increasing in a pattern similar to the Fibonacci sequence (2, 5, 13, 34), where each number is the sum of the previous two differences. For example:

- 2 + 5 = 7 (approximation to 8)
- 5 + 13 = 18 (approximation to 21)

Continuing this pattern:

- 13 + 34 = **47**

Adding this difference to the last number (55):

- 55 + 47 = **144**

Therefore, the next digit in this sequence is likely **144**.

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**Related Questions:**
1. What is a Fibonacci sequence?
2. How can sequences be classified in mathematics?
3. What are arithmetic and geometric sequences?
4. How do recursive sequences work?
5. Can complex sequences be solved using matrices?

**Tip:** Always look for patterns in sequences by checking differences, ratios, or other relationships between consecutive terms.

Explore the pattern in the sequence 1, 3, 8, 21, 55 and discover the next number using principles from recursive sequences and the Fibonacci sequence. Learn about recursive relationships and how to predict the next term in a complex sequence. Suitable for advanced high school students and mathematics enthusiasts.

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