Download 2 - arithmetic exlicit sequence.notebook

2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
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Consider Rowen‛s sequence: 2, 4, 6, 8, …
Assume that the numbers in the
sequence follow the same pattern, what
is the next number?
2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
Student Outcomes:
Students write sequences with explicit
formula. Students learn the structure of
arithmetic sequences.
Vocabulary:
Arithmetic Sequence: A sequence is called arithmetic if
there is a real number d such that each term in the sequence
is the sum of the previous term and d.
Common difference (d) – the difference between the 2
consecutive terms
Explicit formula: formula that can be used to find the value
of any term you want without having to know the value of the
term before
2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
The explicit formula for Arithmetic Sequences
1. Consider Akelia‛s sequence 5, 8, 11, 14, 17, …
a. If you believed in patterns, what might you say is the
next number in the sequence?
b. Write a formula for Akelia‛s sequence to find the nth
term. First use the notation an, then in the notation f(n).
an = a1 + d(n-1)
an is the first term
d is the common difference
f(n) = f(1) +d(n-1)
f(1) is the first term
d is the common difference
2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
c Graph the terms of the sequence as ordered pairs (n, f(n)) on
the coordinate plane. What do you notice about the graph?
d.
If you connected the points, what function would the graph be?
Arithmetic sequences are often referred to as
______________________ sequences.
1. Consider a sequence that follows a “5” pattern:
4, 9, 14, 19, …
a. Write a formula for the nth term of the sequence.
Be sure to specify what value of n your formula
starts with.
b. Using the formula, find the 20th term of the
sequence.
2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
c Graph the terms of the sequence as ordered pairs (n, f(n)) on
the coordinate plane. What do you notice about the graph?
d.
If you connected the points, what function would the graph be?
4. Consider a sequence generated by the
formula f(n) = 3n – 4 starting with n=1.
Generate the terms f(1), f(2), f(3), f(4),
and f(5).
2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
5. The local football team won the championship several
years ago, and since then, ticket prices have been
increasing $20 per year. The year they won the
championship, tickets were $50. Write an explicit
formula for a sequence that will model ticket prices.
6. Consider the arithmetic sequence 13, 24, 35, 46, …
a. Find an explicit form for the sequence in terms of n.
b. Find the 40th term.
c. If the nth term is 299, find the value ofn.
2 ­ arithmetic exlicit sequence.notebook
September 04, 2015
7. Consider the arithmetic sequence 16, 10, 4, -2, …
a. Find an explicit form for the sequence in terms of n.
b. Find the 15th term.
Exit ticket:
Write an explicit formula for the following sequence: ­8,0,8,16,...