96, 320, 800, 1600, ?

Options

A. 640
B. 2666.7
C. 2500
D. 2400

Explanation

To find the missing number in the series: 96, 320, 800, 1600, ?, we can analyze the pattern of the series step by step.

### Step 1: Identify the Pattern
Let's look at the numbers in the series:
- 96
- 320
- 800
- 1600

We can see that each number is increasing. To find a pattern, we will check how each number relates to the previous number.

### Step 2: Calculate the Ratios
1. **From 96 to 320**:
- \( \frac{320}{96} = \frac{320 \div 16}{96 \div 16} = \frac{20}{6} \approx 3.33 \) (not a simple ratio)

2. **From 320 to 800**:
- \( \frac{800}{320} = \frac{800 \div 80}{320 \div 80} = \frac{10}{4} = 2.5 \) (not a simple ratio)

3. **From 800 to 1600**:
- \( \frac{1600}{800} = 2 \)

### Step 3: Identify the Multiplicative Pattern
Now let's look at the multipliers:
- From 96 to 320, we can see it is approximately multiplying by \( \frac{10}{3} \) or \( 3.33 \).
- From 320 to 800, it is multiplying by \( 2.5 \).
- From 800 to 1600, it is multiplying by \( 2 \).

### Step 4: Establish the Next Multiplier
If we observe the pattern of the multipliers:
- The first multiplier is approximately \( \frac{10}{3} \) (or \( 3.33 \)),
- The second multiplier is \( 2.5 \),
- The third multiplier is \( 2 \).

It seems like the multipliers are decreasing. If we assume the next multiplier follows this pattern, we can try \( 1.5 \) (which is \( 0.5 \) less than \( 2 \)).

### Step 5: Calculate the Next Number
Now we can calculate the next number in the series:
- \( 1600 \times 1.5 = 2400 \)

### Conclusion
Thus, the missing number in the series is **2400**.