In each of the following question a number series is given .After the series is given.After the series below it a number is given followed by a,b,c,d and e , you have to complete the series starting with the number given following the sequence of the given series. Then answer the question given below it
11 15 38 126
7 a b c d e
which of the following will come in place of ( c ) ?

Options

A. 102
B. 30
C. 2140
D. 80

Answer

To solve the given problem, we need to identify the pattern in the first series (11, 15, 38, 126) and then apply that pattern to the second series starting with the number 7.

### Step-by-step Solution:

1. **Identify the Pattern in the First Series:**
- The first series is: 11, 15, 38, 126.
- Let's analyze the differences between the numbers:
- From 11 to 15: \(15 - 11 = 4\)
- From 15 to 38: \(38 - 15 = 23\)
- From 38 to 126: \(126 - 38 = 88\)

2. **Look for a Multiplicative Pattern:**
- The differences do not form a simple arithmetic sequence, so let's check for a multiplicative pattern:
- \(11 \times 1 + 4 = 15\)
- \(15 \times 2 + 8 = 38\)
- \(38 \times 3 + 12 = 126\)

3. **Establish the Pattern:**
- It appears that each term is obtained by multiplying the previous term by an increasing integer and then adding an increasing multiple of 4:
- For the first term: Multiply by 1 and add \(4 \times 1\)
- For the second term: Multiply by 2 and add \(4 \times 2\)
- For the third term: Multiply by 3 and add \(4 \times 3\)

4. **Apply the Pattern to the Second Series:**
- The second series starts with 7: \(7, a, b, c, d, e\)
- We will apply the same pattern:
- To find \(a\): \(7 \times 1 + 4 = 11\)
- To find \(b\): \(11 \times 2 + 8 = 30\)
- To find \(c\): \(30 \times 3 + 12 = 102\)

5. **Final Answer:**
- The value of \(c\) is **102**.