The average of first nine multiples of 3 is

Options

A. 12
B. 12.5
C. 15
D. 18.5

Answer

To find the average of the first nine multiples of 3, we can follow these steps:

### Step 1: Identify the first nine multiples of 3
The first nine multiples of 3 are:
- 1st multiple: \(3 \times 1 = 3\)
- 2nd multiple: \(3 \times 2 = 6\)
- 3rd multiple: \(3 \times 3 = 9\)
- 4th multiple: \(3 \times 4 = 12\)
- 5th multiple: \(3 \times 5 = 15\)
- 6th multiple: \(3 \times 6 = 18\)
- 7th multiple: \(3 \times 7 = 21\)
- 8th multiple: \(3 \times 8 = 24\)
- 9th multiple: \(3 \times 9 = 27\)

So, the first nine multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27.

### Step 2: Calculate the sum of these multiples
Now, we need to calculate the sum of these numbers:
\[ 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 \]

Calculating step-by-step:
- \(3 + 6 = 9\)
- \(9 + 9 = 18\)
- \(18 + 12 = 30\)
- \(30 + 15 = 45\)
- \(45 + 18 = 63\)
- \(63 + 21 = 84\)
- \(84 + 24 = 108\)
- \(108 + 27 = 135\)

Thus, the sum of the first nine multiples of 3 is \(135\).

### Step 3: Find the average
The average is calculated by dividing the sum by the number of items. Here, we have 9 multiples:
\[ \text{Average} = \frac{\text{Sum}}{\text{Number of items}} = \frac{135}{9} \]

Calculating this gives:
\[ \frac{135}{9} = 15 \]

### Final Answer
The average of the first nine multiples of 3 is **15**.

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