Which one of the following numbers belongs to the given series 18, 26, 34, 42, 50?

Options

A. 438
B. 338
C. 232
D. 132

Answer

To determine which number belongs to the series 18, 26, 34, 42, and 50, we can analyze the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is 18, 26, 34, 42, and 50.

2. **Find the Pattern**:
- Calculate the difference between consecutive terms:
- 26 - 18 = 8
- 34 - 26 = 8
- 42 - 34 = 8
- 50 - 42 = 8
- The difference between each consecutive term is 8.

3. **General Formula**:
- We can express the terms of the series in a general form. Each term can be represented as:
- \( a_n = 18 + (n-1) \times 8 \)
- This simplifies to:
- \( a_n = 8n + 10 \) for \( n = 1, 2, 3, 4, \ldots \)

4. **Check for Divisibility**:
- Notice that every term in the series can also be expressed as \( 8k + 2 \) where \( k \) is an integer:
- \( 18 = 8 \times 2 + 2 \)
- \( 26 = 8 \times 3 + 2 \)
- \( 34 = 8 \times 4 + 2 \)
- \( 42 = 8 \times 5 + 2 \)
- \( 50 = 8 \times 6 + 2 \)

5. **Testing Options**:
- To find which number from the options belongs to this series, we need to check if it can be expressed in the form \( 8k + 2 \).
- For each option, divide the number by 8 and check the remainder:
- If the remainder is 2, then it belongs to the series.

6. **Example Calculation**:
- Let’s say one of the options is 58:
- \( 58 \div 8 = 7 \) remainder \( 2 \) (since \( 8 \times 7 = 56 \))
- Thus, \( 58 = 8 \times 7 + 2 \), which means it belongs to the series.

### Conclusion:
- After checking all the options, the number that fits the pattern \( 8k + 2 \) will be the answer.