What are the numbers divisible by 1025?

1025, 2050, 3075, 4100, 5125, 6150, 7175, 8200, 9225, 10250, 11275, 12300, 13325, 14350, 15375, 16400, 17425, 18450, 19475, 20500, 21525, 22550, 23575, 24600, 25625, 26650, 27675, 28700, 29725, 30750, 31775, 32800, 33825, 34850, 35875, 36900, 37925, 38950, 39975, 41000, 42025, 43050, 44075, 45100, 46125, 47150, 48175, 49200, 50225, 51250, 52275, 53300, 54325, 55350, 56375, 57400, 58425, 59450, 60475, 61500, 62525, 63550, 64575, 65600, 66625, 67650, 68675, 69700, 70725, 71750, 72775, 73800, 74825, 75850, 76875, 77900, 78925, 79950, 80975, 82000, 83025, 84050, 85075, 86100, 87125, 88150, 89175, 90200, 91225, 92250, 93275, 94300, 95325, 96350, 97375, 98400, 99425

There is a total of 97 numbers (up to 100000) that are divisible by 1025.
The sum of these numbers is 4871825.
The arithmetic mean of these numbers is 50225.

How to find the numbers divisible by 1025?

Finding all the numbers that can be divided by 1025 is essentially the same as searching for the multiples of 1025: if a number N is a multiple of 1025, then 1025 is a divisor of N.

Indeed, if we assume that N is a multiple of 1025, this means there exists an integer k such that:

$k \times 1025 = N$

Conversely, the result of N divided by 1025 is this same integer k (without any remainder):

$k = \frac{N}{1025}$

From this we can see that, theoretically, there's an infinite quantity of multiples of 1025 (we can keep multiplying it by increasingly larger integers, without ever reaching the end).

However, in this instance, we've chosen to set an arbitrary limit (specifically, the multiples of 1025 less than 100000):

1 × 1025 = 1025
2 × 1025 = 2050
3 × 1025 = 3075
...
96 × 1025 = 98400
97 × 1025 = 99425