Ch. 7 Sums and Sequences
7.1 Define and Use Sums and Sequences
A. OBJ: to recognize and write number patterns.
B. Facts/Formulas:
1. A sequence is a function whose domain is a set of
consecutive integers. If a domain is not specified, it is
understood that the domain starts with 1. A sequence can
be specified by an equation, or rule.
2. The values in the range are called the terms of the
sequence.
3. A finite sequence has a limited number of terms. An infinite
sequence continues without stopping.
4. When the terms of a sequence are added together, the
resulting expression is a series.
5. Summation notation, or sigma notation, is used to write a
series.
 2i
a. For example, in the series
, i is the index of
summation, 1 is the lower limit of summation, and 4 is
the upper limit of summation.
4
i 1
C. Examples:
1.
7.2 Arithmetic Series
A. OBJ: to study arithmetic sequences and series
B. FACTS/FORMULAS:
1. In an arithmetic sequence, the difference of
consecutive terms is constant. This constant difference
is called the common difference and is denoted by d.
2. The nth term of an arithmetic sequence with first term
a1 and common difference d is given by:
an = a1 + (n  1)d
3. The expression formed by adding the terms of an
arithmetic sequence is called an arithmetic series. The
sum of the first n terms of an arithmetic series is:
 a  an 

S n  n 1
 2 
C. Examples:
1.
7.3 Geometric Series
A. OBJ: to study geometric sequences and series
B. Facts/Formulas:
1. In a geometric sequence, the ratio of any term to the
previous term is constant. This constant ratio is called the
common ratio and is denoted by r.
2. The nth term of a geometric sequence with first term a1
and common ratio r is given by:
an = anrn1
3. The expression formed by adding the terms of a
geometric sequence is called a geometric series. The sum
of the first n terms of a geometric series with common
ratio
r  1 is:
1 r n 

S n  a1 
 1 r 
C. Examples:
7.4 Sums of Infinite Geometric Series
A. OBJ: to find the sum of infinite geometric series
B.Facts/Formulas:
1. The sum Sn of the first n terms of an infinite series is
called a partial sum.
2. The sum of an infinite geometric series with first term
al and common ratio r is given by
S 
a1
1 r
provided | r | < 1.
3. *** If | r |> 1, the series has no sum.
C. Ex:
7.5 Recursive Rules for Sequences
A. OBJ: to use recursive rules for sequences.
B. Facts/Formulas:
1. A recursive rule gives the beginning term or terms of
a sequence and then a recursive equation that tells
how an is related to one or more preceding terms.
2. Arithmetic sequence: an = an1 + d where d is the
common difference
3. Geometric sequence: an = r an1 where r is the
common ratio
C. EX: