4.4 Arithmetic Sequences
Notes
An arithmetic sequence adds the same common difference $d$ each time: 5, 8, 11, 14, ... has $d = 3$.
- Explicit formula: $a_n = a_1 + (n - 1)d$.
- Recursive formula: $a_1 = 5$, $a_n = a_{n-1} + 3$.
- An arithmetic sequence is a linear function whose domain is the counting numbers.
Practice
What is the common difference of $20, 14, 8, 2, ...$?
Each term is 6 less than the one before.
For $a_n = 4 + (n - 1)5$, what is $a_{10}$?
$4 + 9(5) = 49$.
Which explicit formula fits $7, 10, 13, 16, ...$?
$a_n = 7 + (n - 1)3 = 3n + 4$.
Ready for more? Take the Unit 4 test.