Find the average of first 20 multiples of 9.

Options

A. 94.8
B. 94.7
C. 4.6
D. 94.5

Answer

To find the average of the first 20 multiples of 9, we can follow these steps:

### Step 1: Identify the first 20 multiples of 9
The first 20 multiples of 9 can be calculated by multiplying 9 by the integers from 1 to 20.
- The multiples are:
- 9 × 1 = 9
- 9 × 2 = 18
- 9 × 3 = 27
- 9 × 4 = 36
- 9 × 5 = 45
- 9 × 6 = 54
- 9 × 7 = 63
- 9 × 8 = 72
- 9 × 9 = 81
- 9 × 10 = 90
- 9 × 11 = 99
- 9 × 12 = 108
- 9 × 13 = 117
- 9 × 14 = 126
- 9 × 15 = 135
- 9 × 16 = 144
- 9 × 17 = 153
- 9 × 18 = 162
- 9 × 19 = 171
- 9 × 20 = 180

### Step 2: Calculate the sum of these multiples
To find the sum of the first 20 multiples of 9, we can use the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2} \times (a + l) \]
Where:
- \( n \) = number of terms (20)
- \( a \) = first term (9)
- \( l \) = last term (180)

Calculating:
\[ S_{20} = \frac{20}{2} \times (9 + 180) \]
\[ S_{20} = 10 \times 189 \]
\[ S_{20} = 1890 \]

### Step 3: Calculate the average
The average can be calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Substituting the values:
\[ \text{Average} = \frac{1890}{20} \]

Calculating:
\[ \text{Average} = 94.5 \]

### Final Answer
The average of the first 20 multiples of 9 is **94.5**.

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