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
2 3 9 40.5
4 a b c d e
which of the following will come in place of ( b ) ?

Options

A. 486
B. 81
C. 3645
D. 18

Answer

To solve the problem, we need to analyze the given series and find the pattern that connects the numbers. The series provided is:

2, 3, 9, 40.5

We need to find the value of (b) in the series starting with the number 4:

4, a, b, c, d, e

### Step-by-Step Solution:

1. **Identify the Pattern in the Given Series:**
- The first number is 2.
- The second number is 3, which can be obtained by multiplying 2 by 1.5:
\[ 2 \times 1.5 = 3 \]
- The third number is 9, which can be obtained by multiplying 3 by 3:
\[ 3 \times 3 = 9 \]
- The fourth number is 40.5, which can be obtained by multiplying 9 by 4.5:
\[ 9 \times 4.5 = 40.5 \]

2. **Establish the Multiplication Pattern:**
- The multipliers used are:
- From 2 to 3: Multiply by 1.5
- From 3 to 9: Multiply by 3
- From 9 to 40.5: Multiply by 4.5
- The pattern of multipliers appears to be increasing by 1.5 each time:
- 1.5, 3, 4.5 (which is 1.5 * 3)

3. **Apply the Same Pattern to the New Series:**
- Starting with 4:
- First, we multiply 4 by 1.5:
\[ 4 \times 1.5 = 6 \quad (This is 'a') \]
- Next, we multiply 6 by 3:
\[ 6 \times 3 = 18 \quad (This is 'b') \]
- Then, we multiply 18 by 4.5:
\[ 18 \times 4.5 = 81 \quad (This is 'c') \]
- Finally, we multiply 81 by 6:
\[ 81 \times 6 = 486 \quad (This is 'd') \]

4. **Conclusion:**
- The value of (b) is 18.

### Final Answer:
The value of (b) is **18**.