Arithmetic vs. Geometric
A sequence is arithmetic if a constant is ________ the prior term. An arithmetic
sequence is sometimes called a linear sequence.
A sequence is geometric if a constant is ________ the prior term. A geometric sequence
acts like an exponential function.
Example:
Sequence
Type
(Arithmetic or
Geometric)
Declarations
Explicit
A(1) &
Formula
n>1
Recursive
Formula
-2, 2, 6, 10, …
2, 4, 8, 16, …
1
1
A (1) = 2
A(n + 1) = A(n) + 2
A (1) = 1
A(n + 1) = A(n) ∙
A(n) = 9 – 5n
A(n) = 10(0.1)n - 1
Example: 2, 4, 6, 8, …
Is the sequence arithmetic or geometric?
Write a recursive formula for a sequence that will model the sequence.
Write the explicit formula for the sequence.
1
3
Exercise:
1. 3, 9, 27, 81, …
a. Is the sequence arithmetic or geometric?
b. Write a recursive formula for a sequence that will model the sequence.
(Be sure to declare A(1) and n > 1.)
c. Write the explicit formula for the sequence.
2. 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.
a. Is the sequence arithmetic or geometric?
b. Write a recursive formula for a sequence that will model the sequence.
(Be sure to declare A(1) and n > 1.)
c. Write the explicit formula for the sequence.
3. A radioactive substance decreases in the amount of grams by one third each year.
The starting amount of the substance in a rock is 1,452g.
a. Is the sequence arithmetic or geometric?
b. Write a recursive formula for a sequence that models the amount of the
substance left after the end of each year. (Be sure to declare A(1) and n > 1.)
c. Write the explicit formula for the sequence.
Name: ___________________________________
Algebra I CC
Date: ______
Exit Ticket
List the first 3 terms in the following sequence. Identify them as arithmetic or
geometric.
a. A(n + 1) = A(n) – 5 for n > 1 and A(1) = 9.
1
b. A(n + 1) = A(n) for n > 1 and A(1) = 4
2
Name: ___________________________________
Algebra I CC
Date: ______
Exit Ticket
List the first 3 terms in the following sequence. Identify them as arithmetic or
geometric.
a. A(n + 1) = A(n) – 5 for n > 1 and A(1) = 9.
1
b. A(n + 1) = 2 A(n) for n > 1 and A(1) = 4