1. Sequences and Series 13.3 The arithmetic sequence
DO NOW: Given the sequence 4, 15, 32, 55, 84, 119…
Is it linear or quadratic?
Write a recursive formula.
Write an explicit formula.

2. Arithmetic Sequences Example #1
a n or a(n)
a) Write a recursive definition.
b) Write a closed-form (explicit) definition.
c) Common difference is ___.
a n = a 1 + (n-1)d

3. Example #2: The 10th term of an arithmetic sequence is 146 and the 18th term is 98.
Find the first term and common difference.

4. Example #3: A portion of the arithmetic sequence is given
Example #3: A portion of the arithmetic sequence is given. Fill in blanks.
28, ___, ____, ____, 42
This is also known as finding the arithmetic means.
“Find 3 arithmetic means between 28 and 42.”

5. Arithmetic Series & Sigma Notation Example #4: Write the finite series in Sigma Notation
Finite series – also a partial sum.
S4 = = 20

6. Example #5: Find the partial sum S10 of the first ten terms of the arithmetic sequence.
an = 2 + (n-1) S10 =
The sum of the first n terms, Sn , of the arithmetic sequence an , with common difference d is

7. There’s MORE!
If and a n = a 1 + (n-1)d ,
then Sn =

8. Find the sum of the first 75 terms of the sequence.
Example #6: An arithmetic sequence has a1 = -10 and a common difference of 0.25.
Find the sum of the first 75 terms of the sequence.

9. Arithmetic Series Arithmetic sequence – the list of terms 2,4,6,8,….2n
Arithmetic series – the sum of the list
…+ 2n +…
Finite series – also a partial sum
= 20
Infinite series …+ 2n +…