In each of the following questions a number series is given followed by (a) (b) (c) (d) and (e). You have to complete the series starting with given number, following the sequence of original series and answer the questions that follows the series
3 19 103 439 1381 2887 5 (a) (b) (c) (d) (e) What will come in place of (b)?

Options

A. 139
B. 163
C. 161
D. 157

Answer

To solve the number series given in the question: 3, 19, 103, 439, 1381, 2887, 5 (a) (b) (c) (d) (e), we need to identify the pattern in the series and find the value that will replace (b).

### Step-by-Step Solution:

1. **Identify the Pattern:**
- Let's observe the series:
- From 3 to 19:
- \( 3 \times 6 + 1 = 19 \)
- From 19 to 103:
- \( 19 \times 5 + 8 = 103 \)
- From 103 to 439:
- \( 103 \times 4 + 27 = 439 \)
- From 439 to 1381:
- \( 439 \times 3 + 4 = 1381 \)
- From 1381 to 2887:
- \( 1381 \times 2 + 125 = 2887 \)

2. **Continuing the Pattern:**
- Now, we need to find the next number after 2887.
- Let's denote the last number as \( n = 2887 \).
- We will multiply \( n \) by 2 and add 1:
- \( 2887 \times 2 + 1 = 5775 \)

3. **Finding the Value for (b):**
- The next number in the series should be calculated similarly.
- If we follow the pattern, we can assume the next number after 5775 will be calculated by multiplying by 3 and adding a certain number.
- Let's calculate:
- \( 5775 \times 3 + 4 = 17329 \)

4. **Finalizing the Answer:**
- The value that will replace (b) in the series is **5775**.

### Summary of the Series:
- The complete series is: 3, 19, 103, 439, 1381, 2887, 5775, 17329, ...