Integrated Math 3 / Unit 9: Sequences, Series and Functions Review
9.1 Arithmetic Sequences and Series
Notes
An arithmetic sequence adds the same common difference $d$ each time.
- Explicit rule: $a_n = a_1 + (n - 1)d$.
- Example: $3, 7, 11, \dots$ has $d = 4$, so $a_{20} = 3 + 19(4) = 79$.
- An arithmetic series is the sum of terms: $\displaystyle S_n = \frac{n(a_1 + a_n)}{2}$.
- Example: $\displaystyle 1 + 2 + \dots + 100 = \frac{100(1 + 100)}{2} = 5050$.
Practice
What is the 20th term of the sequence $3, 7, 11, 15, \dots$?
$a_{20} = 3 + 19(4) = 79$.
What is the sum of the first 20 terms of $3, 7, 11, 15, \dots$?
$\displaystyle S_{20} = \frac{20(3 + 79)}{2} = 820$.
Which term of the sequence $4, 9, 14, \dots$ is equal to 99?
$4 + (n - 1)5 = 99$ gives $n - 1 = 19$, so $n = 20$.
Ready for more? Take the Unit 9 test.