Transcript A) An arithmetic sequence is represented by the

Arithmetic Sequences
Objectives:
To identify and extend patterns in
sequences.
To represent arithmetic sequences
using functions notation
*
A wooden post-and-rail fence with two rails is made
as shown. Find the number of pieces of wood needed
to build a 4-section fence, a 5 section fence, and a 6section fence. Suppose you want to build a fence
with 3 rails. How many pieces of wood are needed
for each size fence? Describe the pattern.
Sequence:
an ordered list of numbers that often
form a pattern.
Term of a Sequence:
Each number in the list
Problem #1: Extending Sequences
Describe a pattern in each sequence. What are the
next two terms of each sequence?
A)
B)
Problem #1
Got It?
Describe a pattern in each sequence. What are the
next two terms of each sequence.
1) 5, 11, 17, 23, …
2) 400, 200, 100, 50, …
3) 2, -4, 8, -16, …
4) -15, -11, -7, -3, …
Arithmetic Sequence:
A number sequence formed by adding
a fixed number to each previous term
to find the next.
Common Difference:
The fixed number added to each
previous term in an Arithmetic
Sequence
Problem #2: Identifying an Arithmetic
Sequence
Tell whether the sequence is arithmetic. If
it is, what is the common difference?
A) 3, 8, 13, 18, …
B)
-3, -7, -10, -14, …
Problem #2
Got It?
Tell whether each sequence is arithmetic. If
it is, what is the common difference?
1) 8, 15, 22, 30,…
2) 7, 9, 11, 13, …
3) 10, 4, -2, -8, …
4) 2, -2, 2, -2, …
Recursive Formula:
A function rule that relates each term
of a sequence after the first to the
ones before it
Consider the sequence 7, 11, 15, 19…
Consider the sequence 7, 11, 15, 19…
Common Difference:
Problem #3: Writing a Recursive Formula
A) Write a recursive formula for the
arithmetic sequence below. What is the
value of the 8th term?
70, 77, 84, 91,…
Problem #3: Writing a Recursive Formula
B) Write a recursive formula for the
arithmetic sequence below. What is the
value of the 7th term?
3, 9, 15, 21…
Problem #3
Got It?
Write a recursive formula for each
arithmetic sequence. What is the 9th
term of each sequence?
1) 23, 35, 47, 59, …
2) 7.3, 7.8, 8.3, 8.8, …
3) 97, 88, 79, 70, …
*Homework
Textbook Page 279; #10 – 34 Even
Continued…
Objectives:
To represent arithmetic sequences
using functions notation
Explicit Formula:
A function rule that relates each term
of a sequence to the term number
The nth term of an arithmetic sequence with
first term A(1) and common difference d is
given by:
Problem #4: Writing an Explicit Formula
A) An online auction works as shown
below. Write an explicit formula to
represent the bids as an arithmetic
sequence. What is the 12th bid?
Problem #4: Writing an Explicit Formula
B)
A subway pass has a starting value of
$100. After one ride, the value of the pass
is $98.25. After two rides, its value is
$96.50. After three rides, its value is
$94.75. Write an explicit formula to
represent the remaining value on the card
as an arithmetic sequence. What is the
value of the pass after 15 rides?
Problem #4: Writing an Explicit Formula
C) Using your answer from B, how many
rides can be taken with the $100
pass?
Problem #4
Got It?
Justine’s grandfather puts $100 in a savings
account for her on her first birthday. He
puts $125, $150, and $175 into the account
on her next 3 birthdays. If this pattern
continues, how much will Justine’s
grandfather put in the savings account on
her 12th birthday?
Problem #5: Writing an Explicit
Formula From a Recursive Formula
A) An arithmetic sequence is represented
by the recursive formula A(n)=A(n – 1) + 12.
If the first term of the sequence is 19,
write the explicit formula.
Problem #5: Writing an Explicit
Formula From a Recursive Formula
B) An arithmetic sequence is represented
by the recursive formula A(n)=A(n – 1) + 2.
If the first term of the sequence is 21,
write the explicit formula.
Problem #5
Got It?
An arithmetic sequence is represented by
the recursive formula A(n)=A(n – 1) + 7. If
the first term of the sequence is 2, write
the explicit formula.
Problem #6: Writing a Recursive
Formula From an Explicit Formula
A) An arithmetic sequence is
represented by the explicit formula
A(n)= 32 + (n – 1)(22). What is the
recursive formula?
Problem #6: Writing a Recursive
Formula From an Explicit Formula
B) An arithmetic sequence is
represented by the explicit formula
A(n)= 76 + (n – 1)(10). What is the
recursive formula?
Problem #6
Got It?
An arithmetic sequence is represented by
the explicit formula A(n)=1 +(n – 1)(3).
Write the recursive formula.
*Homework
Textbook Page 278 – 280; #1 – 8,
36 – 52 Even