What should come in place of the question mark (?) in the following number series? `10" "15" "15" "12.5" "9.375" "6.5625`

Options

A. `4.375`
B. `3.2375`
C. `4.6275`
D. `3.575`

Answer

To find the next term in the series `10, 15, 15, 12.5, 9.375, 6.5625`, we will analyze the pattern in the series step by step.

### Step 1: Write down the series
The series is as follows:
- 10
- 15
- 15
- 12.5
- 9.375
- 6.5625

### Step 2: Identify the pattern
Let's look at the changes between the terms:
1. From 10 to 15:
- \( 10 \times \frac{3}{2} = 15 \)
2. From 15 to 15:
- \( 15 \times 1 = 15 \)
3. From 15 to 12.5:
- \( 15 \times \frac{5}{6} = 12.5 \)
4. From 12.5 to 9.375:
- \( 12.5 \times \frac{15}{16} = 9.375 \)
5. From 9.375 to 6.5625:
- \( 9.375 \times \frac{21}{32} = 6.5625 \)

### Step 3: Establish the multiplication pattern
The multipliers are:
- \( \frac{3}{2} \) (or 1.5)
- \( 1 \) (or \( \frac{15}{15} \))
- \( \frac{5}{6} \)
- \( \frac{15}{16} \)
- \( \frac{21}{32} \)

### Step 4: Find the next multiplier
The numerators of the multipliers are increasing in a specific pattern:
- \( 3, 15, 5, 15, 21 \)

The denominators are:
- \( 2, 15, 6, 16, 32 \)

To find the next term, we can observe that the numerators and denominators seem to follow a pattern. The next numerator can be inferred to be \( 7 \) (following the pattern of odd numbers), and the next denominator can be inferred to be \( 8 \) (following the pattern of powers of 2).

### Step 5: Calculate the next term
Now, we will calculate the next term using the last term \( 6.5625 \):
- Next term = \( 6.5625 \times \frac{7}{8} \)

Calculating:
- \( 6.5625 \times 0.875 = 5.7421875 \)

### Conclusion
Thus, the next term in the series is approximately \( 5.7421875 \).

### Final Answer
The term that should come in place of the question mark (?) is **5.7421875**.

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