Download Section 11.2 Defining Functions Using Sums: Arithmetic

Section 11.2
Defining Functions Using Sums:
Arithmetic Series
• Consider the following sequences
1. 3, 5, 7, 9, 
2. 1, 3, 6, 10, 15, 
3. 20, 40, 80, 160, 
4. 5, 2,  1,  4, 
• Determine which are arithmetic by examining the
pattern
• Often times we may have a finite arithmetic
sequence
– In this case we can find the sum of the sequence
• Consider a theater with 40 rows of seats. The first
row contains 18 seats and each row after that
contains 2 more.
– How many seats are in the 40th row?
– What if we want to know the total number of seats in the
theater
• In this case we are looking for the summation of the
first 40 terms of an arithmetic sequence
• We denote this as Sn
• Let’s take a look at this sum by looking at the sum
of pairs of numbers (i.e. a1 + a40 , a2 + a39, etc.)
• The general formula for the sum of the first n terms
of an arithmetic series is given by
n
S n  a1  an 
2
• For the following sequences, determine whether or
not they are arithmetic. If they are, find a100 and S100
1
1. a n 
n
3 1 1
2.
, ,  ,
4 4 4
3. an  3  3n
4. 0.2, 0.02, 0.002, 
Sigma Notation
• When we are summing up the first n terms of a
sequence, we use sigma notation
n
S n   ai  a1  a2    an
i 1
• Let’s write the summations from the last slide
using sigma notation
3 1 1
1.
, ,  ,
4 4 4
2. an  3  3n