Integrated Math 1 / Unit 4: Linear Functions and Arithmetic Sequences
4.5 Arithmetic Sequences
Notes
An arithmetic sequence adds the same number, the common difference $d$, each time.
- Explicit formula: $a_n = a_1 + (n - 1)d$. Recursive: $a_n = a_{n-1} + d$.
- An arithmetic sequence is a linear function whose inputs are whole numbers $n = 1, 2, 3, \dots$
- Example: $4, 9, 14, 19, \dots$ has $d = 5$ and $a_{10} = 4 + 9(5) = 49$.
- Use $n - 1$, not $n$, because the first term has no jumps yet.
Practice
What is the 10th term of the sequence $4, 9, 14, 19, \dots$?
$d = 5$, so $a_{10} = 4 + (10 - 1)(5) = 49$.
Which formula gives the sequence $7, 4, 1, -2, \dots$?
$a_n = 7 - 3(n - 1) = 10 - 3n$. Check: $n = 1$ gives 7.
A sequence has $a_1 = 2$ and $a_n = a_{n-1} + 6$. What is $a_4$?
The terms are 2, 8, 14, 20.
Ready for more? Take the Unit 4 test.