What is the average of first 17 odd numbers?

Options

A. 16
B. 17
C. 18
D. 19

Answer

To find the average of the first 17 odd numbers, we can follow these steps:

### Step 1: Identify the first 17 odd numbers
The first 17 odd numbers are:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33.

### Step 2: Calculate the last term (17th term)
The nth term of the sequence of odd numbers can be calculated using the formula:
\[ a_n = a + (n - 1) \cdot d \]
where:
- \( a \) is the first term (1 in this case),
- \( n \) is the number of terms (17),
- \( d \) is the common difference (2 for odd numbers).

Substituting the values:
\[ a_{17} = 1 + (17 - 1) \cdot 2 \]
\[ a_{17} = 1 + 16 \cdot 2 \]
\[ a_{17} = 1 + 32 \]
\[ a_{17} = 33 \]

### Step 3: Calculate the average
The average of a series can be calculated using the formula:
\[ \text{Average} = \frac{\text{Sum of terms}}{\text{Number of terms}} \]

However, we can also find the average directly using the first and last terms:
\[ \text{Average} = \frac{\text{First term} + \text{Last term}}{2} \]
Here, the first term is 1 and the last term is 33.

Substituting these values:
\[ \text{Average} = \frac{1 + 33}{2} \]
\[ \text{Average} = \frac{34}{2} \]
\[ \text{Average} = 17 \]

### Final Answer
The average of the first 17 odd numbers is **17**.

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