9 13 21 37 69 ? 261

Options

A. 121
B. 135
C. 47
D. 133

Explanation

To solve the series: 9, 13, 21, 37, 69, ?, 261, we will follow these steps:

### Step 1: Identify the series
We have the series: 9, 13, 21, 37, 69, ?, 261.

### Step 2: Calculate the differences between consecutive terms
Let's find the differences between each pair of consecutive terms:

- Difference between 13 and 9:
\( 13 - 9 = 4 \)

- Difference between 21 and 13:
\( 21 - 13 = 8 \)

- Difference between 37 and 21:
\( 37 - 21 = 16 \)

- Difference between 69 and 37:
\( 69 - 37 = 32 \)

Now we have the differences: 4, 8, 16, 32.

### Step 3: Analyze the pattern in the differences
The differences we calculated are:
4, 8, 16, 32.

We can see that each difference is doubling the previous one:
- \( 4 \times 2 = 8 \)
- \( 8 \times 2 = 16 \)
- \( 16 \times 2 = 32 \)

### Step 4: Predict the next difference
Following the pattern, the next difference should be:
\( 32 \times 2 = 64 \).

### Step 5: Calculate the missing number
To find the missing number, we add this difference (64) to the last known term (69):
- Missing number = \( 69 + 64 = 133 \).

### Step 6: Verify the next term
Next, we need to check if this fits the series by calculating the difference between 261 and the missing number (133):
- Difference = \( 261 - 133 = 128 \).

Now, checking the pattern, the next difference after 64 should be \( 64 \times 2 = 128 \), which matches our calculation.

### Conclusion
The missing number in the series is **133**.

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