M3L2
Algebra I –
Name
NOTES: Explicit Formulas for Sequences Date
What is meant by an “Explicit Formula”?
Example: Find an explicit formula for the sequence {10, 15, 20, 25, 30, 35, …}
Term
Number
Subscript
Notation
Term
Function
Notation
We can write this explicit formula in two ways:
Subscript Notation:
Function Notation:
To summarize the process of writing an explicit formula for an arithmetic sequence:
1. Determine if the sequence is arithmetic (Do you add, or subtract, the same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create an explicit formula using the pattern of the first term added to the product of the common difference and
one less than the term number.
an= a1 + d (n - 1)
an = the nth term in the sequence
a1 = the first term in the sequence
n = the term number
d = the common difference.
first term = 10, common difference = 5
{10, 15, 20, 25, 30, 35, ...} explicit formula: an= 10 + 5(n - 1)
= 10 + 5n - 5 = 5 + 5n or 5n + 5
How could we have used this new information to create a function for the previous example?
M3L2
Example: Find an explicit formula for the sequence {3, 6, 12, 24, 48, 96, …}
Term
Number
Term
Subscript
Notation
Function
Notation
To summarize the process of writing an explicit formula for a geometric sequence:
1. Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
2. Find the common ratio. (The number you multiply or divide.)
3. Create an explicit formula using the pattern of the first term multiplied by the common ratio raised to a power of
one less than the term number.
an = the nth term in the sequence
a1 = the first term in the sequence
n = the term number
r = the common ratio
{3, 6, 12, 24, 48, 96, ...}
first term = 10, common ratio = 2
explicit formula: an= 3 • 2n-1
We can write this explicit formula in two ways:
Subscript Notation:
Function Notation: