How many four-digit numbers are divisible by 5?

There are 1800 four-digit numbers that are divisible by 5.

To understand why, let's examine the properties of four-digit numbers and divisibility by 5.

Four-Digit Numbers and Divisibility by 5

Four-digit numbers range from 1000 to 9999. A number is divisible by 5 if its last digit is either 0 or 5.

According to the provided reference, the first four-digit number divisible by 5 is 1000, and the last one is 9995. This sequence forms an arithmetic progression (AP) where:

• The first term (T1) is 1000.
• The last term (Tn) is 9995.
• The common difference (d) is 5.

We can calculate the total number of such numbers using the following AP formula:

  Tn = T1 + (n-1) * d

Where 'n' is the number of terms in the sequence. In our case:

``` 9995 = 1000 + (n-1) * 5 ```

Solving for n:

8995 = (n-1) * 5
1799 = n - 1
n = 1800

Therefore there are 1800 four-digit numbers that are divisible by 5.

Here's a breakdown of the solution provided in the reference:

• The reference correctly identifies the first (1000) and last (9995) four-digit numbers divisible by 5.
• It correctly notes that these numbers form an AP with a common difference of 5.
• The calculation `n = 1999 + 1 - 200 = 1800` mentioned in the reference refers to an alternative method of calculating the same thing. The numbers divisible by 5 fall at every 5th increment of the number line. If we divide the range of four-digit numbers by 5 we can determine how many of those numbers are divisible by 5. * The largest four digit number is 9999. If we divide it by 5, we get 1999.8. The largest four digit number evenly divisible by 5 is therefore 1999 * 5 = 9995. * The smallest four digit number is 1000, and if we divide it by 5 we get 200. * Subtract the two results: 1999 - 200 = 1799. Add 1 to account for the inclusive nature of the first term in the sequence. 1799 + 1 = 1800
• Both methods provide the same result: 1800 four-digit numbers divisible by 5.