Average of first eight multiples of 8 is

Options

A. 36
B. 46
C. 32
D. 72

Answer

To find the average of the first eight multiples of 8, we can follow these steps:

### Step 1: Identify the first eight multiples of 8.
The first eight multiples of 8 are:
- 1st multiple: \(8 \times 1 = 8\)
- 2nd multiple: \(8 \times 2 = 16\)
- 3rd multiple: \(8 \times 3 = 24\)
- 4th multiple: \(8 \times 4 = 32\)
- 5th multiple: \(8 \times 5 = 40\)
- 6th multiple: \(8 \times 6 = 48\)
- 7th multiple: \(8 \times 7 = 56\)
- 8th multiple: \(8 \times 8 = 64\)

So, the first eight multiples of 8 are: **8, 16, 24, 32, 40, 48, 56, 64**.

### Step 2: Calculate the sum of these multiples.
Now, we need to find the sum of these multiples:
\[ 8 + 16 + 24 + 32 + 40 + 48 + 56 + 64 \]

Calculating this step by step:
- \(8 + 16 = 24\)
- \(24 + 24 = 48\)
- \(48 + 32 = 80\)
- \(80 + 40 = 120\)
- \(120 + 48 = 168\)
- \(168 + 56 = 224\)
- \(224 + 64 = 288\)

Thus, the sum of the first eight multiples of 8 is **288**.

### Step 3: Calculate the average.
The average is calculated by dividing the sum of the observations by the number of observations (which is 8 in this case):
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{288}{8} \]

Calculating this gives:
\[ \frac{288}{8} = 36 \]

### Conclusion:
The average of the first eight multiples of 8 is **36**.

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