14.1 Arithmetic Sequences OBJ: Find terms of arithmetic sequences.
Key Vocabulary 9.2 Arithmetic Sequences A sequence in ...
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1 9.2 Arithmetic Sequences How can you write a rule (formula/equation) for an arithmetic sequence? Key Vocabulary Arithmetic sequence A sequence in which the difference between consecutive terms is a constant. Common difference The value of the difference in arithmetic sequences. EXAMPLE 1 Identify arithmetic sequences Tell whether the sequence is arithmetic and give the common difference a. –4, 1, 6, 11, 16, . . . b. 3, 5, 9, 15, 23, . . . Equations for Arithmetic Sequences a n =a 1 + (n – 1)d a n : nth term a 1 : 1 st term d: common difference
Transcript of Key Vocabulary 9.2 Arithmetic Sequences A sequence in ...
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9.2 Arithmetic
Sequences
How can you write a rule
(formula/equation) for an
arithmetic sequence?
Key Vocabulary
Arithmetic sequence
A sequence in which the difference between
consecutive terms is a constant.
Common difference
The value of the difference in arithmetic
sequences.
EXAMPLE 1 Identify arithmetic sequences
Tell whether the sequence is arithmetic and give
the common difference
a. –4, 1, 6, 11, 16, . . .b. 3, 5, 9, 15, 23, . . .
Equations for Arithmetic
Sequences
an=a1 + (n – 1)d
an: nth term
a1: 1st term
d: common difference
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EXAMPLE 2 Write a rule for the nth term
a. 4, 9, 14, 19, . . . b. 60, 52, 44, 36, . . .
Write an explicit rule for the nth term of the
sequence. Then write a recursive rule.
a.
EXAMPLE 3 Write a rule given a term and common difference
One term of an arithmetic sequence is a19 = 48. The
common difference is d = 3.
a. Write a rule for the nth term. b. Graph the sequence.
EXAMPLE 4 Write a rule given two terms
Two terms of an arithmetic sequence are a8 = 21 and
a27 = 97. Find a rule for the nth term.
GUIDED PRACTICE for Examples 2, 3, and 4
Write a rule for the nth term of the arithmetic
sequence. Then find a20.
2. 17, 14, 11, 8, . . .
3. a11 = –57, d = –7
4. a7 = 26, a16 = 71
WB Example 3 p 349
Homework: WB p 351 #1-13
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Summary of Steps to Find the Explicit
Rule for Arithmetic Sequences
Find d by subtracting the given terms and dividing by the spaces between terms If you are given d you may skip this step
Find a1 by plugging in an, n, and d into the equation an = a1 + (n – 1)d Remember an is the answer given, n is the little subscript
number
If you are given a1 you may skip this step
Fill in a1 and d into the equation an = a1 + (n – 1)dand clean it up by distributing then adding like pieces
Switching between Explicit and
Recursive Form
The easiest way to switch between forms is to
create a table
Ex) f(n) = 2n + 3 is in ___________ form
To switch to ____________ form make a table
n f(n)
1
2
3
4
Switching between Recursive and
Explicit Form
The easiest way to switch between forms is to
create a table
Ex) f(1) = 5; f(n) = f(n-1) + 3; n ≥ 2 is in ___________
form
To switch to ____________ form make a table
n f(n)
1
2
3
4
Recognizing the Relationship
between Recursive and Explicit Form
Look back at the last two slides
What do you notice?
