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
4 13 40 135 522 2765 2 (a) (b) (c) (d) (e) What will come in place of (c)?

Options

A. 123
B. 133
C. 127
D. 131

Answer

To solve the given number series: 4, 13, 40, 135, 522, 2765, we need to identify the pattern and then find the values for (a), (b), (c), (d), and (e), specifically focusing on what comes in place of (c).

### Step-by-Step Solution:

1. **Identify the Pattern in the Series:**
- The series starts with 4 and each subsequent number seems to be generated by a specific multiplication and addition pattern.
- Let's analyze the transitions:
- From 4 to 13
- From 13 to 40
- From 40 to 135
- From 135 to 522
- From 522 to 2765

2. **Calculate Each Step:**
- **From 4 to 13:**
- \( 4 \times 3 + 1 = 12 + 1 = 13 \)
- **From 13 to 40:**
- \( 13 \times 3 + 1 = 39 + 1 = 40 \)
- **From 40 to 135:**
- \( 40 \times 3 + 15 = 120 + 15 = 135 \)
- **From 135 to 522:**
- \( 135 \times 4 - 18 = 540 - 18 = 522 \)
- **From 522 to 2765:**
- \( 522 \times 5 + 5 = 2610 + 155 = 2765 \)

3. **Establishing the Next Series:**
- Now we need to start a new series beginning with 2:
- **Starting with 2:**
- \( 2 \times 1 + 9 = 2 + 9 = 11 \) (This will be the first number in the new series)
- **Next Number:**
- \( 11 \times 2 + 7 = 22 + 7 = 29 \)
- **Next Number:**
- \( 29 \times 3 + 5 = 87 + 5 = 92 \)
- **Next Number:**
- \( 92 \times 4 + 3 = 368 + 3 = 371 \)
- **Next Number:**
- \( 371 \times 5 + 1 = 1855 + 1 = 1856 \)

4. **Finding the Value for (c):**
- The series generated from starting with 2 is:
- 2, 11, 29, 92, 371, 1856
- In this series, the value corresponding to (c) is **92**.

### Final Answer:
The value that comes in place of (c) is **92**.