1. Arithmetic Sequences and Series
Chapter 8.2

2. Arithmetic Sequence
An Arithmetic Sequence has a constant difference between any two consecutive terms.
The Common Difference is denoted by d.

3. Arithmetic or not…
1.) 7, 10, 13, 16, …
2.) 15, 8, 1, -6, …
3.) 8, 4, 2, 1, …
4.) 15, 9, 3, -3, …

4. Arithmetic Sequence Rule
where an is the nth term, a1 is the first term in the sequence, n is the number of terms, and d is the common difference.
Note: You need the beginning number and the common difference to write a rule.
𝑎 𝑛 = 𝑎 1 +(𝑛−1)𝑑

5. Using the Rule… a1 = 3, d = 5 𝑎 𝑛 = 𝑎 1 +(𝑛−1)𝑑
Write a rule for each sequence.
𝑎 𝑛 = 𝑎 1 +(𝑛−1)𝑑
Ex. 1.) 3, 8, 13, 18, …
a1 = 3, d = 5
Find the 20th term.
𝑎 𝑛 =3+(𝑛−1)5 𝑎 𝑛 =3+5𝑛−5 𝑎 𝑛 =5𝑛−2
𝑎 1 =15 𝑑=−7
Ex 2.) 15, 8, 1, -6, …

6. Write a rule given the common difference and a term in the sequence.
𝑎 19 =−45 𝑑=−3
Find the rule for this sequence.
Now use the information to write the rule.

7. Writing a rule given two terms
Now we have too many unknowns.
We have the 5th term is -43.
And we have the 12th term is -8.
Now we have produced 2 equations with 2 unknowns.

8. Now we can solve for the 2 missing variables using system of equations.
d=5, now substitute 5 in for d in one of
the original equations to find a1.
Now substitute d=5 and a1 = -63 into the Arithmetic Sequence Rule formula.

9. Sum of an Arithmetic Sequence.
;where n is the number of
terms, a1 is the first term of the sequence,
an is the last term of the sequence, and S
is the sum of the sequence.
n = (Top – Bottom) + 1
= (8-1) + 1 = = 8 terms
First term a1 = 2(1) - 3= -1
Last term an = 2(8) - 3= 13

10. Sum Continued…
−1+13 2
S = = = 8(6) = 48

11. HOMEWORK 5/19/16
PAGE 422
1, 2, 6 – 38 even, 44 – 58 even, 59