10 18 34 ? 130 258

Options

A. 32
B. 60
C. 66
D. 68

Explanation

To find the missing number in the series 10, 18, 34, ?, 130, 258, we need to identify the pattern in the sequence.

### Step 1: Identify the pattern
Let's look at the differences between consecutive terms:

- From 10 to 18:
\[ 18 - 10 = 8 \]

- From 18 to 34:
\[ 34 - 18 = 16 \]

Now, we can see that the differences themselves are increasing. Let's write down the differences:
- First difference: 8
- Second difference: 16

### Step 2: Analyze the differences
Next, let's look at the next difference:
- If we observe the pattern, it seems that the difference doubles each time:
- The first difference is 8 (which is \(2^3\))
- The second difference is 16 (which is \(2^4\))

Following this pattern, the next difference should be:
- Third difference: \(2^5 = 32\)

### Step 3: Calculate the missing number
Now, we add this difference to the last known term (34):
\[ 34 + 32 = 66 \]

### Step 4: Verify the next terms
Now let's check if this fits with the next known term (130):
- From 66 to 130:
\[ 130 - 66 = 64 \]
This difference (64) is \(2^6\), which continues the pattern.

Now, let's check the difference from 130 to 258:
\[ 258 - 130 = 128 \]
This difference (128) is \(2^7\), which also fits the pattern.

### Conclusion
Thus, the missing number in the series is **66**.