Sum of consecutive numbers (Maths series)

Maths meets programming

Helping my son prepare for the 11+ test reignited my interest in maths. With over couple of decades in programming, I naturally started applying what I was learning—turning formulas into code. This blog is my way of documenting that journey.

These are simple problems, often solved and available on coding platforms, but this is my personal exploration of learning and implementation.

To find sum of n given numbers. For example, 1,2,3,4,5 will be 1 + 2 + 3 + 4 + 5 = 15.

Problem

It looks easy for small list of numbers but quickly becomes a difficult task as list grows.

Solution

To find the sum of numbers like 1, 2, 3, ..., n, the quickest thought was to loop through numbers but instead of looping through them, use this elegant formula:

sum = (n * (n + 1)) / 2;

where n is the largest number in the list i.e. for 1,2,3,4...100, n = 100`

Here’s a small JavaScript method:

function sum(...args) {
  const n = Math.max(...args);
  return (n * (n + 1)) / 2;
}

Example:

sum(1, 2, 3, 4, 5); // 15

Others in the Maths series

• Find Greatest Common Factor (GCF)