400 240 144 86.4 51.84 31.104 ?

Options

A. 19.2466
B. 17.2244
C. 16.8824
D. 18.6624

Explanation

To find the missing number in the series: 400, 240, 144, 86.4, 51.84, 31.104, ?, we can follow these steps:

### Step 1: Identify the pattern
First, observe the series. The numbers seem to be decreasing, and they are also in decimal form. This suggests that we might be dividing the previous number by a certain factor.

### Step 2: Calculate the ratio between consecutive terms
Let's calculate the ratio of the first two terms:
- \( \frac{400}{240} = \frac{400 \div 80}{240 \div 80} = \frac{5}{3} \)

Now, let's check the next pair:
- \( \frac{240}{144} = \frac{240 \div 48}{144 \div 48} = \frac{5}{3} \)

Next, check the next pair:
- \( \frac{144}{86.4} = \frac{144 \div 28.8}{86.4 \div 28.8} = \frac{5}{3} \)

Next, check the next pair:
- \( \frac{86.4}{51.84} = \frac{86.4 \div 17.28}{51.84 \div 17.28} = \frac{5}{3} \)

Finally, check the last pair:
- \( \frac{51.84}{31.104} = \frac{51.84 \div 10.368}{31.104 \div 10.368} = \frac{5}{3} \)

### Step 3: Establish the multiplication factor
From the calculations above, we can see that each term is obtained by multiplying the previous term by \( \frac{3}{5} \).

### Step 4: Calculate the missing number
To find the next number after 31.104, we multiply it by \( \frac{3}{5} \):
- \( 31.104 \times \frac{3}{5} = 31.104 \times 0.6 \)

Calculating this:
- \( 31.104 \times 0.6 = 18.6624 \)

### Conclusion
Thus, the missing number in the series is **18.6624**.

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