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 find the value of \( x \) in the given sequence \( 0, 1, 1, 2, 3, 5, 8, 13, x, 34 \), we can observe that this sequence resembles the Fibonacci sequence. In the Fibonacci sequence, each number is the sum of the two preceding numbers.

Let's break down the solution step by step:

### Step 1: Identify the pattern
The Fibonacci sequence starts with \( 0 \) and \( 1 \), and each subsequent number is the sum of the two previous numbers.

### Step 2: Write down the known values
The sequence provided is:
- \( 0 \)
- \( 1 \)
- \( 1 \)
- \( 2 \)
- \( 3 \)
- \( 5 \)
- \( 8 \)
- \( 13 \)
- \( x \)
- \( 34 \)

### Step 3: Calculate the missing value \( x \)
To find \( x \), we look at the two numbers before it in the sequence:
- The two numbers before \( x \) are \( 13 \) and \( 21 \) (which we will calculate next).

Using the Fibonacci rule:
\[ x = 13 + 8 \]
Calculating this gives:
\[ x = 21 \]

### Step 4: Verify the next number in the sequence
Now, we check if the next number \( 34 \) follows the same pattern:
\[ 34 = 21 + 13 \]
This is correct.

### Conclusion
Thus, the value of \( x \) is \( 21 \).

### Final Answer
The value of \( x \) is \( 21 \).

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