Consecutive Numbers

The sum of the first $n$ consecutive natural numbers is given by the formula:

$S = 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2}$

This is a special case of the sum of an arithmetic progression (AP), where the first term $a = 1$ and the common difference $d = 1$. For any AP with first term $a$, last term $l$, and $n$ terms:

$S = \frac{n(a + l)}{2}$

Important properties

• The sum of consecutive numbers forms a triangular number.

• The formula works for any sequence of consecutive numbers starting from 1.

• For sequences not starting at 1, adjust the formula or use the AP sum formula.