1. Warm Up Complete the table… Recursive Formula Sequence
Explicit Formula
6,8,10,12…

2. Arithmetic Sequences and Partial Sums
Keeper
GSE Accelerated Pre-Calculus

3. Arithmetic Sequences
A sequence is arithmetic if there exists a number d, called the common difference, such that an+1 = an + d

4. Example For each of the following arithmetic sequences, identify
the first term, a1, and the common difference, d.
a) 6, 10, 14, 18, 22, …
b) 0, 6, 12, 18, 24, … c)

5. nth Term of an Arithmetic Sequence
The nth term of an arithmetic sequence is given by the formula:
an = a1 + (n  1)d

6. Example
Find the 11th term of the arithmetic sequence
2, 6, 10, 14, …

7. Another Example
The 3rd term of an arithmetic sequence is 5, and the 9th term is 37. Find a1 and d and construct the sequence.

8. Sum of the First n Terms
The formula for the sum of the first n terms of an arithmetic sequence is given by:

9. Example Find the sum of the first 11 terms of the arithmetic sequence
16, 12, 8, 4, …

10. Another Example
Find the sum:

11. Application
An orchestra consists of 8 rows of musicians. The first row has 5 musicians, the second row has 7 musicians, and the third row has 9 musicians.
a) How many musicians are in the last row?
b) What is the total number of musicians in the orchestra?