1. Unit 3: Linear and Exponential Functions
Coordinate Algebra
Sequences

2. Arithmetic sequence
A sequence in which the difference between consecutive terms is constant.
A sequence such as
1, 5, 9, 13, 17, 21 or
12, 7, 2, -3, -8, -13
which has a constant difference between terms.

3. Recursive formula
Pertaining to or using a rule or procedure that can be applied repeatedly. It builds onto the previous term.
2, 5, 8, 11, 14…
an = an – 1 + d
an = an – 1 + 3

4. Explicit formula
An explicit formula expresses the nth term of a sequence in terms of n. It can be used to find any term in the sequence based on the term number.
Let an = 2n + 5 for positive integers n.
If n = 7, then a7 = 2(7) + 5 = 19.

5. arithmetic sequence an = a1 + (n – 1)d
The first term is a1, the common difference is d, and the number of terms is n.

6. arithmetic sequence Example: 3, 7, 11, 15, 19 a1 = 3, d = 4, n = 5
The explicit formula is
an = 3 + (n – 1)·4
= 4n – 1

7. Identifying an arithmetic sequence
To decide whether a sequence is arithmetic, find the differences of consecutive terms.
If the difference is always the same, the sequence is arithmetic.
If the differences are not constant, the sequence is not arithmetic.

8. Writing a rule for the nth term
Identify the 1st term or a1.
Find the common difference.
Write the general rule using
an = a1 + (n – 1)d
inserting the values of a1 and d.
Simplify

9. Finding the nth term given a term and the common difference
Begin by finding the first term using
an = a1 + (n – 1)d
and substituting for an, n and d.
Write the general rule using
inserting the values of a1 and d.
Simplify

10. geometric sequence
an exponential function that results in a sequence of numbers separated by a constant ratio
constant ratio: the number multiplied by each consecutive term in a geometric sequence