Question

What is a simple formula to solve a math sequence? Or a couple formulas if possible? Thanks!

Answer 1

2 normal types of sequences:

1. arythmetic sequences: each term is the same distance to the next term, example, 2,4,6,8, distance is 2

2. geometric sequences: the ratio of consecutive terms is the same, example: 2,4,8,16, ratio is 4:2=2:1, 2/1=2


the nth term is denoted by
`a_(n)`
the first term is represented by
`a_(1)`

for arythmetic sequences, the nth tem is

`a_(n)=a_(1)(n-1)d` where d=distance between each term

for geometric sequences the nth term is
[tex] a_{n}=a_{1}r^{n-1} where r=ratio betwen consecutive terms