Find the average of first seven prime numbers.

Options

A. 8
B. 9
C. `8 1/7`
D. `8 2/7`

Answer

To find the average of the first seven prime numbers, we can follow these steps:

### Step 1: Identify the first seven prime numbers
The first seven prime numbers are:
1. 2
2. 3
3. 5
4. 7
5. 11
6. 13
7. 17

### Step 2: Calculate the sum of these prime numbers
Now, we need to sum these numbers:
\[ 2 + 3 + 5 + 7 + 11 + 13 + 17 \]

Calculating step by step:
- \(2 + 3 = 5\)
- \(5 + 5 = 10\)
- \(10 + 7 = 17\)
- \(17 + 11 = 28\)
- \(28 + 13 = 41\)
- \(41 + 17 = 58\)

So, the total sum is \(58\).

### Step 3: Divide the sum by the number of terms
To find the average, we divide the sum by the number of prime numbers, which is \(7\):
\[ \text{Average} = \frac{\text{Sum of prime numbers}}{\text{Number of prime numbers}} = \frac{58}{7} \]

### Step 4: Perform the division
Now, we perform the division:
\[ 58 \div 7 = 8 \quad \text{(with a remainder of 2)} \]
This can be expressed as:
\[ 8 \frac{2}{7} \]

### Final Answer
Thus, the average of the first seven prime numbers is:
\[ 8 \frac{2}{7} \]

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