what should come in place of question mark( ?) in the following number series ?
`10" "17" "48" "165" "688" "3475" "?`

Options

A. 27584
B. 25670
C. 21369
D. 20892

Answer

To solve the number series: 10, 17, 48, 165, 688, 3475, ?, we need to identify the pattern in the series. Let's break it down step by step.

### Step 1: Identify the pattern between the numbers
- The first number is **10**.
- The second number is **17**.

To go from 10 to 17:
\[ 10 \times 1 + 7 = 17 \]

### Step 2: Continue with the next number
Now, from **17** to **48**:
\[ 17 \times 2 + 14 = 48 \]

### Step 3: Check the next transition
Next, from **48** to **165**:
\[ 48 \times 3 + 21 = 165 \]

### Step 4: Continue with the next number
From **165** to **688**:
\[ 165 \times 4 + 28 = 688 \]

### Step 5: Check the next transition
From **688** to **3475**:
\[ 688 \times 5 + 35 = 3475 \]

### Step 6: Identify the next number in the series
Now, we need to find the next number after **3475**. Following the established pattern:
- The next multiplication factor is **6**.
- The next addition should be **42** (the pattern of addition is increasing by 7 each time: 7, 14, 21, 28, 35, 42).

So, we calculate:
\[ 3475 \times 6 + 42 \]

### Step 7: Perform the calculation
First, calculate \( 3475 \times 6 \):
\[ 3475 \times 6 = 20850 \]

Now, add **42**:
\[ 20850 + 42 = 20892 \]

Thus, the number that should come in place of the question mark is **20892**.

### Final Answer:
The answer is **20892**.

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