What is the average of first 30 multiples of 9?
A. 142
B. 138.5
C. 139.5
D. 143.5

Options

A. B
B. A
C. D
D. C

Answer

To find the average of the first 30 multiples of 9, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the first 30 multiples of 9**:
The first multiple of 9 is \(9 \times 1 = 9\), the second is \(9 \times 2 = 18\), and so on. The 30th multiple is \(9 \times 30 = 270\).

2. **List the multiples**:
The first 30 multiples of 9 are:
\[ 9, 18, 27, \ldots, 270 \]

3. **Use the formula for the average**:
The average is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of terms}}{\text{Total number of terms}} \]

4. **Calculate the sum of the first 30 multiples of 9**:
We can use the formula for the sum of an arithmetic series:
\[ S_n = \frac{n}{2} \times (a + l) \]
where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.

Here, \(n = 30\), \(a = 9\), and \(l = 270\).

Substituting these values into the formula:
\[ S_{30} = \frac{30}{2} \times (9 + 270) = 15 \times 279 = 4185 \]

5. **Calculate the average**:
Now that we have the sum, we can find the average:
\[ \text{Average} = \frac{4185}{30} \]

6. **Perform the division**:
Dividing \(4185\) by \(30\):
\[ 4185 \div 30 = 139.5 \]

### Final Answer:
Thus, the average of the first 30 multiples of 9 is \(139.5\).