By using the concept of arithmetic series, it can be calculated that
y - x = 1250
What is arithmetic series?
Arithmetic series are those series whose difference between two consecutive terms are same.
The odd integers forms an arithmetic series
For the sum of first 25 odd integer
First odd integer = 1
25th odd integer = 49
Sum of first 25 odd integers = [tex]\frac{25}{2}(1 + 49)[/tex] = 625
x = 625
For the sum of first 50 odd integers
First odd integer = 1
50th odd integer = 99
Sum of first 50 odd integers = [tex]\frac{50}{2}(1 + 99)[/tex] = 2500
Sum of next 25 odd integers = 2500 - 625 = 1875
y = 1875
y - x = 1875 - 625 = 1250
To learn more about arithmetic series, refer to the link-
https://brainly.com/question/6561461
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