The sum of all numbers between 100 and 1000 that are divisible by 5 is 98,450.
Explanation
To find the sum of numbers between 100 and 1000 that are divisible by 5, we need to identify the first and last numbers in this range that are divisible by 5, and then use the arithmetic series formula.
Identifying the Series
- First number divisible by 5 greater than 100: 105
- Last number divisible by 5 less than 1000: 995
So, we are summing the series: 105, 110, 115, ..., 995
Using the Arithmetic Series Formula
The sum of an arithmetic series is given by:
S = (n/2) * (a + l)
where:
- S is the sum of the series
- n is the number of terms in the series
- a is the first term
- l is the last term
Calculating the Number of Terms (n)
We can find the number of terms using the formula:
l = a + (n - 1) * d
where:
- l is the last term (995)
- a is the first term (105)
- d is the common difference (5)
995 = 105 + (n - 1) 5
890 = (n - 1) 5
178 = n - 1
n = 179
Calculating the Sum (S)
Now we can calculate the sum:
S = (n/2) (a + l)
S = (179/2) (105 + 995)
S = (179/2) (1100)
S = 179 550
S = 98450
Conclusion
According to the reference provided, the sum of all natural numbers between 100 and 1000 which are multiples of 5 is indeed 98,450.
