math ch4: sequences and series

sequence

each number in a sequence is called a

the difference between one term and the next term is constant and denoted by d. in other words, we add the same value every time. this is a

terms between two nonconsecutive terms in the sequence. this is

example of arithemetic mean

each term is found by multiplying the previous term by a constant called common ratio and denoted by r. this is a

to find the nth term in an arithmetic sequence, we use the rule:

to find the nth term in a geometric sequence, we use the rule

terms between two nonconsecuttive terms in the geometric sequence

if there are three consecutive terms, the geometric mean is

series

rule for the sum of terms in a finite arithmetic sequence

sigma notation and explanation of terms

the number of terms in the series is found by

sum of terms for a finite geometric series

if absolute r is greater than or equal to 1, the series is —— and sum is

if absolute r is less than or equal to 1, the series is ———— and the sum is