Lesson 11.1
Sequences and Series
Warm Up:
Comprehension Quiz:
1) Who were Titius and
Bode? page
German
Astronomers
Read
690…
Close your books
2) What does their sequence model?
The distances between the
sun and the planets
3) What did they find at the distance
corresponding to the fifth bode
number?
Ceres
4) The asteroid belt containing Ceres
lies between which 2 planets?
Mars and Jupiter
By reading page 691, define the following terms:
Vocabulary:
Sequence: An ordered list of numbers, called terms
Terms: The numbers in a sequence
Infinite Sequence: A sequence that continues without end
Ellipsis: Three dots, used to indicate an infinite sequence
Finite Sequence: A sequence that has a last term
Explicit Formula: A formula that defines the nth term, or
general term, of a sequence
n
1
2
3
4
5
6
tn
1
7
17
31
49
71
The first six terms are: 1, 7, 17, 31, 49, and 71
TRY THIS, page 691
t1  1 and tn  3tn1  1, where n  2
tn  3tn1  1
t1  1
t2  3t1  1  3(1)  1  2
t3  3t2  1  3(2)  1  5
t4  3t3  1  3(5)  1  14
t5  3t4  1  3(14)  1  41
t6  3t5  1  3(41)  1  122
The first six terms are 1, 2, 5, 14, 41, 122
Planet
5th: Ceres
6th: Jupiter
7th: Saturn
8th: Uranus
Bode
Number
Distance from the planet to Sun
By reading page 693, define the following terms:
Vocabulary:
Series: An expression that indicates the sum of terms of a sequence
Summation notation: A way to express a series in abbreviated
form, using the Greek letter sigma
Sigma:

Values of n from 1 to
5 are called the index
5
 2n
n 1
Explicit formula for the general
term of the related sequence
TRY THIS, page 693
5
a.
 4k
k 1
4  8  12  16  20
 60
1 4
b.  k
2 k 1
1
1  2  3  4 
2
1
 10 
2
5
Homework:
Practice 11.1