What is the arithmetic mean of first 8 multiples of 13?

Options

A. 55.4
B. 58.5
C. 72.5
D. 61.8

Answer

To find the arithmetic mean of the first 8 multiples of 13, we can follow these steps:

### Step 1: Identify the first 8 multiples of 13
The first 8 multiples of 13 are:
1. \( 1 \times 13 = 13 \)
2. \( 2 \times 13 = 26 \)
3. \( 3 \times 13 = 39 \)
4. \( 4 \times 13 = 52 \)
5. \( 5 \times 13 = 65 \)
6. \( 6 \times 13 = 78 \)
7. \( 7 \times 13 = 91 \)
8. \( 8 \times 13 = 104 \)

So, the first 8 multiples of 13 are: 13, 26, 39, 52, 65, 78, 91, 104.

### Step 2: Calculate the sum of these multiples
Now, we will sum these multiples:
\[ 13 + 26 + 39 + 52 + 65 + 78 + 91 + 104 \]

Calculating this step-by-step:
- \( 13 + 26 = 39 \)
- \( 39 + 39 = 78 \)
- \( 78 + 52 = 130 \)
- \( 130 + 65 = 195 \)
- \( 195 + 78 = 273 \)
- \( 273 + 91 = 364 \)
- \( 364 + 104 = 468 \)

Thus, the sum of the first 8 multiples of 13 is \( 468 \).

### Step 3: Calculate the arithmetic mean
The arithmetic mean (average) is calculated by dividing the sum of the terms by the number of terms. Here, the number of terms is 8.

\[ \text{Arithmetic Mean} = \frac{\text{Sum of terms}}{\text{Number of terms}} = \frac{468}{8} \]

Calculating this gives:
\[ \frac{468}{8} = 58.5 \]

### Conclusion
The arithmetic mean of the first 8 multiples of 13 is \( 58.5 \).