Honors Precalculus Notes--Chapter 10, Sequences, Induction, and Probability
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Course
Precalculus
Institution
Junior / 11th Grade
Chapter 10 notes for 11th grade Honors Precalculus from an A+ student. Includes definitions on course materials, graphs displaying concepts, numerous example problems including answers, equations, and step-by-step instructions designed to make learning a breeze! Chapter features 4 moduels, includi...
An infinite
sequence { an } is a function whose domain is the set of positive integers The function values or terms of the are
.
, ,
sequence
represented by
A ,
,
A 2
,
A3
,
Ay ,
. . .
, Ang . . .
Sequences whose domains consist
only of the first n positive integers are called finite sequences .
Example
write first four terms of the nth term term
the
sequence whose ,
or
general ,
is
given
an
=
2n -15
To find the first four terms ,
we replace n in the formula with 1,2 , 3, and 4 .
A
,
= 211 ) -15 Az
-
-
2. (2) + S a 3=213 ) -15 a 4=2143+5
=
2+5 = 4+5 = 6+5 =
8+5
= 7 = 9 = 11 =
13
Example
write first four terms of the nth term term
the
n
sequence whose ,
or
general ,
is
given
C- 1)
an
'
271
To find the first four terms ,
we replace n in the formula with 1,2 , 3, and 4 .
12 13 14
'
-
I - -
-
- - - -
A, =
2 't l Az :
22+1 A. 3=23+1 Ay
-
-
24+1
-
l l - l l
- - - -
=
2+1 =
4+1 =
8+1 =
16+1
l
f
l l
-
- - -
-
=
3 =
5 = =
17
Recursion Formulas
A recursion formula defines the nth term of a
sequence as a function of the previous term .
* Uses the previous term to find the next term
Example
Find the first four terms of the in which a. =3 an an =
2am -15 for n
? 2
sequence , .
.
=3 Az Zaz +5 Zaz +5
Zay -15
-
A Az Ay
-
- : -
, , , ,
. .
.
2A , -15 Zaz -15 Zaz
'
=
-15=213
= -
) -15 =
2111 ) -15 =
2127 ) -15
= 11 =
27 =
59
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