What is the average of first 29 even numbers?

Options

A. 30
B. 31
C. 32
D. 33

Answer

To find the average of the first 29 even numbers, we can follow these steps:

### Step 1: Identify the first 29 even numbers
The first 29 even numbers are:
2, 4, 6, ..., 58.
These can be represented as 2n where n = 1, 2, 3, ..., 29.

### Step 2: Calculate the sum of the first 29 even numbers
The formula for the sum of the first N even numbers is:
\[ \text{Sum} = N \times (N + 1) \]
For N = 29:
\[ \text{Sum} = 29 \times (29 + 1) = 29 \times 30 = 870 \]

### Step 3: Calculate the average
The average is calculated using the formula:
\[ \text{Average} = \frac{\text{Sum}}{N} \]
Substituting the values we have:
\[ \text{Average} = \frac{870}{29} \]

### Step 4: Simplify the average calculation
Calculating the average:
\[ \text{Average} = 30 \]

### Final Answer
The average of the first 29 even numbers is **30**.

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