2015­11­4 geometric sequences.notebook
November 04, 2015
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HW Answers
1) d = ­3 an = 38 ­ 3n
2) d = ­20 an = 17 ­ 20n
3) d = ­30 an = ­4 ­ 30n
4) d = ­10 an = ­20 ­ 10n
5) d = ­2 an = ­5 ­ 2n
6) d = 5 an = 4 + 5n
7) ­4, 3, 10, 17, 24 a34 = 227
8) ­35, ­135, ­235, ­335, ­435 a39 = ­3835
9) ­9.2, ­11.3, ­13.4, ­15.5, ­17.6 a27 = ­63.8
10) 15/8, 19/8, 23/8, 27/8, 31/8 a23 = 103/8
11) 28, 38, 48, 58, 68 an = 18 + 10n
12) ­38, ­138, ­238, ­338, ­438 an = 62 ­ 100n
13) ­34, ­44, ­54, ­64, ­74 an = ­24 ­ 10n
14) 35, 39, 43, 47, 51 an = 31 + 4n N
2015­11­4 geometric sequences.notebook
November 04, 2015
Lesson 3: Explicit Formula for Geometric
Sequences
Student Outcomes:
­ Students will be able to identify if a sequence is geometric or not
­Students will be able to derive an explicit formula for an geometric sequence
Geometric Sequence- is a sequence in which there is
a real number r such that each
term of the sequence is the product
of the previous term and r.
Example
1,
3,
3
3
3
3
9,
27,
81, ...
r is called the common ratio
2015­11­4 geometric sequences.notebook
November 04, 2015
Geometric or not????
4, 16, 64, 256....
100, 10, 1, .1, .01, .001.....
1, ­1, 1, ­1, 1, ­1.....
8, 2, 1/2, 1/8, 1/32.....
Explicit Formula For Geometric Sequence
an = a1(r)n-1
nth term
1st term
common ratio
ex. 5, 25, 125, 625....
Find the 12th term of the sequence
2015­11­4 geometric sequences.notebook
November 04, 2015
To find any term in an geometric sequence
an = a1(r)n-1
1) Identify the first term, or a1
2) Find the common ratio
3) Set up and simplify the explicit formula
4) Substitute for n what number term you are trying to find
ex. Find the 10th term of the sequence 6, 12, 24, 48.....
Find the explicit formula.
Then find the a13
­2, 8, ­32, 128....
an = ­2 (­4) n­1
a13 = ­33,554,432
an = a1(r)n-1
2015­11­4 geometric sequences.notebook
Write the explicit formula
November 04, 2015
an = a1(r)n-1
16, 8, 4, 2, 1, 1/2.......
Let's look at a graph of the sequence
1, 3, 9, 27.....
2015­11­4 geometric sequences.notebook
November 04, 2015