sequence and series formulas

arithmetic sequence

a_n=a₁+d(n-1)

arithmetic series

s_n=n((a₁+a_n)/2)

arithmetic sequence

a_n=a₁+d(n-1)

arithmetic series

s_n=n((a₁+a_n)/2)

geometric sequence

a_n=a(r)^n-1

geometric series

s_n=a₁((1-rⁿ)/1-r)

infinite geometric sums

s_n=a₁/1-r

|r|>1 → no sum

0>|r|>1 → sum

repeating decimal

whatever is repeating/one “9” for every repeating value

recursive arithmetic

a_n=a_n-1+d

recursive geometric

a_n=a_n-1(r)