Mathematics
Mathematics
Problem
Find the sum of all consecutive integers from 25 to 110, both numbers being included. (i) How many integers are being added? (ii) Hence, calculate the required sum.Intuitive explanation
This is about using the arithmetic series formula instead of adding 86 numbers by hand. The key insight is that consecutive integers form a perfectly symmetric pattern: the first and last terms always sum to the same value as the second and second-to-last, and so on. Count how many pairs you can make, then multiply by that constant sum—this gives you the total instantly.
Intuitive explanation
This is about using the arithmetic series formula instead of adding 86 numbers by hand. The key insight is that consecutive integers form a perfectly symmetric pattern: the first and last terms always sum to the same value as the second and second-to-last, and so on. Count how many pairs you can make, then multiply by that constant sum—this gives you the total instantly.