What is the average of the first six (positive) odd numbers each of which is divisible by 7?

Options

A. 42
B. 43
C. 47
D. 49

Answer

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

### Step 1: Identify the first six positive odd numbers divisible by 7.
The positive multiples of 7 are:
- 7 (1st multiple)
- 14 (2nd multiple, even)
- 21 (3rd multiple)
- 28 (4th multiple, even)
- 35 (5th multiple)
- 42 (6th multiple, even)
- 49 (7th multiple)
- 56 (8th multiple, even)
- 63 (9th multiple)
- 70 (10th multiple, even)
- 77 (11th multiple)

From the above, the odd multiples of 7 are:
1. 7
2. 21
3. 35
4. 49
5. 63
6. 77

### Step 2: Sum the identified numbers.
Now, we will sum these six numbers:
- 7 + 21 = 28
- 28 + 35 = 63
- 63 + 49 = 112
- 112 + 63 = 175
- 175 + 77 = 252

So, the total sum of these numbers is 252.

### Step 3: Calculate the average.
To find the average, we will divide the sum by the number of observations (which is 6):
\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} = \frac{252}{6} = 42 \]

### Final Answer:
The average of the first six positive odd numbers each of which is divisible by 7 is **42**.

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