Given below is a finite sequence of numbers with an unknown x: 0,1, 1, 2, 3, 5, 8, 13, x, 34, The value of x is

Options

A. 21
B. 20
C. 19
D. 17

Answer

To solve the problem, we need to identify the pattern in the given sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, x, 34.

### Step-by-Step Solution:

1. **Identify the Sequence**: The given numbers are 0, 1, 1, 2, 3, 5, 8, 13, x, 34. This resembles the Fibonacci sequence, where each number is the sum of the two preceding numbers.

2. **Check the Fibonacci Pattern**:
- The Fibonacci sequence starts with 0 and 1.
- The next numbers are calculated as follows:
- 0 + 1 = 1
- 1 + 1 = 2
- 1 + 2 = 3
- 2 + 3 = 5
- 3 + 5 = 8
- 5 + 8 = 13

3. **Calculate the Missing Number (x)**:
- Following the Fibonacci pattern, the next number after 13 should be:
- 8 + 13 = 21
- Therefore, x = 21.

4. **Verify the Next Number**:
- Continuing the pattern, the number after x (which is 21) should be:
- 13 + 21 = 34
- This matches the last number in the sequence.

5. **Conclusion**: The value of x is 21.

### Final Answer:
The value of x is **21**.

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