What will be the average of the first 7 positive odd numbers divisible by 5?

Options

A. 45
B. 35
C. 40
D. 32

Answer

To find the average of the first 7 positive odd numbers that are divisible by 5, we can follow these steps:

### Step 1: Identify the first 7 positive odd numbers divisible by 5.
The positive odd numbers divisible by 5 can be found by starting from 5 and adding 10 each time (since the difference between consecutive odd numbers divisible by 5 is 10).

- The first odd number divisible by 5 is **5**.
- The second odd number divisible by 5 is **15** (5 + 10).
- The third odd number divisible by 5 is **25** (15 + 10).
- The fourth odd number divisible by 5 is **35** (25 + 10).
- The fifth odd number divisible by 5 is **45** (35 + 10).
- The sixth odd number divisible by 5 is **55** (45 + 10).
- The seventh odd number divisible by 5 is **65** (55 + 10).

Thus, the first 7 positive odd numbers divisible by 5 are: **5, 15, 25, 35, 45, 55, 65**.

### Step 2: Calculate the sum of these numbers.
Now, we need to find the sum of these numbers:

\[ 5 + 15 + 25 + 35 + 45 + 55 + 65 \]

Calculating the sum step by step:

- \(5 + 15 = 20\)
- \(20 + 25 = 45\)
- \(45 + 35 = 80\)
- \(80 + 45 = 125\)
- \(125 + 55 = 180\)
- \(180 + 65 = 245\)

So, the total sum is **245**.

### Step 3: Calculate the average.
To find the average, we divide the sum by the number of terms (which is 7):

\[ \text{Average} = \frac{\text{Sum}}{\text{Number of terms}} = \frac{245}{7} \]

Calculating this gives:

\[ \frac{245}{7} = 35 \]

### Final Answer:
The average of the first 7 positive odd numbers divisible by 5 is **35**.

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