A must know formula,

Sum of numbers from 1 to n
= 1/2 * n * (n + 1)

For example, sum of numbers from 1 to 10
= 1/2 * 10 * 11
= 55

Sum of numbers from 5 to 95
= Sum of numbers from 1 to 95, then - 1 - 2 - 3 - 4
= 1/2 * 95 * 96 - 1 - 2 - 3 - 4
= 4560 - 1 - 2 - 3 - 4
= 4550

Thanks for your advice. Need time to digest!

A bit of context :

This formula only works if

① your numbers are consecutive i.e bigger than the previous number by 1

② your first number starts with 1

If you had this for example instead

1 + 4 + 7 + 10 + 13 + ... + 94 + 97 + 100

The above formula would not work as your number of numbers is not 100.

For such patterns you can use this formula:


Sum = ½ x (2a + (n-1)d)

where a is your first number, d is the difference between every 2 numbers (also known as common difference) and n is the number of numbers.