What will come in place of the '?' in the given series.
9, 5, 6, 10.5, 23, ?

Options

A. 160
B. 165
C. 170
D. 175

Explanation

To find the missing number in the series 9, 5, 6, 10.5, 23, ?, we can analyze the pattern of the numbers step by step.

### Step 1: Identify the pattern between the numbers
- The first number is 9, and it decreases to 5.
- The second number is 5, which increases to 6.
- The third number is 6, which increases to 10.5.
- The fourth number is 10.5, which increases to 23.

### Step 2: Calculate the operations between the numbers
1. From 9 to 5:
- The operation can be seen as: \( 9 \times \frac{1}{2} + 0.5 = 4.5 + 0.5 = 5 \)

2. From 5 to 6:
- The operation is simply: \( 5 + 1 = 6 \)

3. From 6 to 10.5:
- The operation can be seen as: \( 6 \times 1.5 + 1.5 = 9 + 1.5 = 10.5 \)

4. From 10.5 to 23:
- The operation can be seen as: \( 10.5 \times 2 + 2 = 21 + 2 = 23 \)

### Step 3: Identify the next operation
Now, we can see a pattern in the multipliers and the added values:
- The multipliers are: \( \frac{1}{2}, 1, 1.5, 2 \)
- The added values are: \( 0.5, 1, 1.5, 2 \)

Following this pattern, the next multiplier should be \( 2.5 \) and the next added value should be \( 2.5 \).

### Step 4: Calculate the missing number
Now we apply this to the last known number:
- From 23, the next number will be calculated as follows:
\[ 23 \times 2.5 + 2.5 \]
- First, calculate \( 23 \times 2.5 = 57.5 \)
- Then add \( 2.5 \): \( 57.5 + 2.5 = 60 \)

### Conclusion
Thus, the missing number in the series is **60**.

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