What is the sum of all three-digit numbers which are divisible by 15?

Given:

We need to find the sum of all three-digit numbers divisible by 15.

Formula Used:

Sum of an arithmetic series: S = (n/2) × (first term + last term)

Solution:

To find the sum of all three-digit numbers divisible by 15, we need to determine the range of numbers and calculate their sum.

Find the first three-digit number divisible by 15.

The smallest three-digit number divisible by 15 is 105.

Find the last three-digit number divisible by 15.

The largest three-digit number divisible by 15 is 990.

Determine the number of terms in the series.

To find the number of terms in the series, we need to calculate the number of three-digit numbers divisible by 15.

The first three-digit number divisible by 15 is 105.

The last three-digit number divisible by 15 is 990.

Using the formula to find the number of terms:

Number of terms = ((last term - first term) / common difference) + 1

Number of terms = ((990 - 105)/15) + 1

Number of terms = (885/15) + 1

Number of terms = 59 + 1

Number of terms = 60

Step 4: Calculate the sum of the series.

Using the formula for the sum of an arithmetic series:

Sum = (number of terms/2) × (first term + last term)

Sum = (60/2) × (105 + 990)

Sum = 30 × 1095

Sum = 32,850

Therefore, the sum of all three-digit numbers divisible by 15 is 32,850.