sequences and series

how is common ratio found

divide a term by the previous term

ex.

a₃ / a₂

arithmetic sequence

a_n = a₁+(n-1)d

d= common difference

sum of finite arithmetic sequence with n terms

S_n= n/2(a₁+a_n)

the nth term of a geometric sequence

a_n=a₁r^n-1

r is the common ratio

sum of finite geometric sequence

(common ratio r is not 1)

sum of infinite geometric series

|r| < 1