The average of 7 consecutive numbers is 20. The smallest of these numbers is:

Options

A. 25
B. 18
C. 21
D. 17

Answer

To find the smallest of 7 consecutive numbers whose average is 20, we can follow these steps:

### Step 1: Define the smallest number
Let the smallest of the 7 consecutive numbers be represented as \( x \).

### Step 2: Express the 7 consecutive numbers
The 7 consecutive numbers can be expressed as:
- \( x \) (smallest)
- \( x + 1 \)
- \( x + 2 \)
- \( x + 3 \)
- \( x + 4 \)
- \( x + 5 \)
- \( x + 6 \)

### Step 3: Calculate the sum of these numbers
The sum of these 7 consecutive numbers can be calculated as:
\[ x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6) \]
This simplifies to:
\[ 7x + (0 + 1 + 2 + 3 + 4 + 5 + 6) = 7x + 21 \]

### Step 4: Use the average to set up an equation
The average of these numbers is given as 20. The average can be calculated by dividing the sum by the number of terms (which is 7):
\[ \text{Average} = \frac{\text{Sum}}{7} = \frac{7x + 21}{7} \]
Setting this equal to 20 gives us the equation:
\[ \frac{7x + 21}{7} = 20 \]

### Step 5: Solve for \( x \)
To eliminate the fraction, multiply both sides by 7:
\[ 7x + 21 = 140 \]
Now, subtract 21 from both sides:
\[ 7x = 140 - 21 \]
\[ 7x = 119 \]
Now, divide by 7:
\[ x = \frac{119}{7} = 17 \]

### Conclusion
The smallest of these 7 consecutive numbers is \( \boxed{17} \).

---