How many numbers between 55 and 555 including both the extreme values are divisible by 5?

Options

A. 100
B. 111
C. 101
D. none of these

Answer

To find how many numbers between 55 and 555 (including both extremes) are divisible by 5, we can follow these steps:

### Step 1: Identify the first and last terms
The first number in the range that is divisible by 5 is 55, and the last number in the range that is divisible by 5 is 555.

### Step 2: Establish the sequence
The numbers divisible by 5 between 55 and 555 form an arithmetic progression (AP) where:
- The first term \( a = 55 \)
- The last term \( l = 555 \)
- The common difference \( d = 5 \)

### Step 3: Use the formula for the nth term of an AP
The nth term of an AP can be calculated using the formula:
\[ l = a + (n - 1) \cdot d \]
Substituting the known values:
\[ 555 = 55 + (n - 1) \cdot 5 \]

### Step 4: Solve for \( n \)
First, subtract 55 from both sides:
\[ 555 - 55 = (n - 1) \cdot 5 \]
\[ 500 = (n - 1) \cdot 5 \]

Next, divide both sides by 5:
\[ n - 1 = \frac{500}{5} \]
\[ n - 1 = 100 \]

Now, add 1 to both sides to find \( n \):
\[ n = 100 + 1 \]
\[ n = 101 \]

### Conclusion
There are **101 numbers** between 55 and 555 that are divisible by 5.

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