Download 4 - geometric explicit sequence.notebook

4 ­ geometric explicit sequence.notebook
September 09, 2015
Do Now:
Consider Charlie‛s sequence: 2, 4, 8, 16, …
Assume that the numbers in the sequence follow the same pattern, what is the next
number?
Please take out your homework
Homework Answers:
1) f(n + 1) = f(n) + 7, f(1) = 14 for n > 1
2) not arithmetic
3) not arithmetic
4) f(n + 1) = f(n) ­ 10, f(1) = ­101 for n > 1
5) f(n + 1) = f(n) ­ 2.5, f(1) = 10 for n > 1
4 ­ geometric explicit sequence.notebook
September 09, 2015
Geometric Explicit Sequences
Student Outcomes:
Students learn the structure of a geometric explicit sequences.
NYS Standard: F.IF.1, F.IF.2, F.IF.3, F.BF.1.a, F.LF.2,
Vocabulary:
Geometric Sequence: A sequence is called geometric if there is a real number r such that each term in the sequence is the product of the previous
term and r.
Common Ratio (r) – 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
4 ­ geometric explicit sequence.notebook
September 09, 2015
The explicit formula for Geometric Sequences
1.
Consider Annalise‛s sequence 3, 9, 27…
a.
If you believed in patterns, what might you say is the next number in the sequence?
b.
Write a formula for Annalise‛s sequence to find the nth term. Use the in the notation f(n).
To find the nth term f(n) : f(n) = f(1) (r)n‐1
f(1) is the first term r is the common ratio
4 ­ geometric explicit sequence.notebook
September 09, 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?
n
d.
eG
If you connected the points, what function would the graph be?
Geometric sequences are often referred to as ______________________
sequences.
1. Consider a sequence that follows the following
pattern: 2, 4, 8, 16,32,...
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 10th term of the
sequence.
4 ­ geometric explicit sequence.notebook
September 09, 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?
n
d.
If you connected the points, what function would the graph be?
Geometric sequences are often referred to as
Geometric sequences are often referred to as ______________________
sequences.
4. Consider a sequence generated by the formula f(n) = 3(2)n-1
starting with n=1. Generate the terms f(1), f(2), f(3), f(4),
and f(5).
4 ­ geometric explicit sequence.notebook
September 09, 2015
5. A radioactive substance decreases in the amount of
grams by one third each year. If the starting amount
of the substance in a rock is 1,452 g, write a explicit
formula for a sequence that models the amount of the
substance left after the end of each year. Is the
sequence arithmetic or geometric?
4 ­ geometric explicit sequence.notebook
September 09, 2015
7. Consider the arithmetic sequence 200, -100, 50, -25 …
a. Find an explicit form for the sequence in terms of n.
b. Find the 15th term.
Exit:
Write the explicit formula for the
geometric sequence:
5,-20,80,-320,...
4 ­ geometric explicit sequence.notebook
September 09, 2015