1, 3, 10, 21, 64, 129,256, 777

Options

A. 10
B. 21
C. 129
D. 256

Explanation

To solve the problem, we need to identify the pattern in the given series: 1, 3, 10, 21, 64, 129, 256, 777. We will analyze the series step by step.

### Step 1: Identify the pattern
Let's observe the series:
1, 3, 10, 21, 64, 129, 256, 777.

We can see that the numbers are increasing, but the increments are not consistent. This suggests that a multiplication and addition pattern might be at play.

### Step 2: Analyze the first few terms
1. Start with the first term: **1**
- Multiply by **2** and add **1**:
\[ 1 \times 2 + 1 = 2 + 1 = 3 \]

2. Next term: **3**
- Multiply by **3** and add **1**:
\[ 3 \times 3 + 1 = 9 + 1 = 10 \]

3. Next term: **10**
- Multiply by **2** and add **1**:
\[ 10 \times 2 + 1 = 20 + 1 = 21 \]

4. Next term: **21**
- Multiply by **3** and add **1**:
\[ 21 \times 3 + 1 = 63 + 1 = 64 \]

### Step 3: Continue the pattern
5. Next term: **64**
- Multiply by **2** and add **1**:
\[ 64 \times 2 + 1 = 128 + 1 = 129 \]

6. Next term: **129**
- Multiply by **3** and add **1**:
\[ 129 \times 3 + 1 = 387 + 1 = 388 \]

7. Next term: **388**
- Multiply by **2** and add **1**:
\[ 388 \times 2 + 1 = 776 + 1 = 777 \]

### Step 4: Compare with the given series
Now, let's compare the calculated terms with the given series:
- The series we calculated is: 1, 3, 10, 21, 64, 129, 388, 777.
- The given series is: 1, 3, 10, 21, 64, 129, 256, 777.

### Step 5: Identify the odd one out
From our analysis, we see that instead of **256**, the correct term should be **388**. Therefore, **256** is the odd one out.

### Conclusion
The odd one out in the series is **256**.

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