Revision sheet · Mathematics

Sequences and progressions

The n-th term of an arithmetic progression (a linear pattern): $a_{n} = a + (n - 1) d$
Sum of the first n natural numbers (triangular numbers): $S = \frac{n ( n + 1 )}{2}$
The n-th term of a geometric progression: $t_{n} = a r^{n - 1}$
Sum of the first n terms of an arithmetic progression: $S = \frac{n}{2} (2 a + (n - 1) d)$
Sum of an arithmetic progression from its first and last terms: $S = \frac{n}{2} (a + l)$