You are given two series in two rows. In the first row, a full series is given which follows a specific pattern. The second row has a series, similar to the first series but only first element of this series is produced followed by (A), (B), (C), (D) and (E) for the subsequent elements. You have to complete the series starting with a given number and answer the question that follows.
`{:("6","9","27","121.5","729",),("8","A","B","C","D","E"):}`
What will come in place of C?

Options

A. 7290
B. 36
C. 972
D. 162

Explanation

To solve the problem, we need to identify the pattern in the first series and then apply that pattern to the second series to find the value that comes in place of C.

### Step-by-Step Solution:

1. **Identify the Pattern in the First Series:**
The first series is: 6, 9, 27, 121.5, 729.
- From 6 to 9:
- \( 6 \times 1.5 = 9 \)
- From 9 to 27:
- \( 9 \times 3 = 27 \)
- From 27 to 121.5:
- \( 27 \times 4.5 = 121.5 \)
- From 121.5 to 729:
- \( 121.5 \times 6 = 729 \)

The multipliers are: 1.5, 3, 4.5, and 6. We can see that each multiplier increases by 1.5.

2. **Establish the Pattern:**
The multipliers can be expressed as:
- First term: \( 1.5 \)
- Second term: \( 1.5 + 1.5 = 3 \)
- Third term: \( 3 + 1.5 = 4.5 \)
- Fourth term: \( 4.5 + 1.5 = 6 \)

So, the pattern is to multiply by increasing values of 1.5.

3. **Apply the Pattern to the Second Series:**
The second series starts with 8: 8, A, B, C, D, E.
- To find A:
- \( 8 \times 1.5 = 12 \) (So, A = 12)
- To find B:
- \( 12 \times 3 = 36 \) (So, B = 36)
- To find C:
- \( 36 \times 4.5 = 162 \) (So, C = 162)

4. **Final Answer:**
The value that comes in place of C is **162**.