1. Warm Up Write an explicit formula for the following sequences.
5, 7, 9, 11, 13,
1, 3, 9, 27, 81,

2. Answers Write an explicit formula for the following sequences.
5, 7, 9, 11, 13,
an = 2n + 3
2. 1, 3, 9, 27, 81,
an = 1 • 3 (n-1)

3. Series and Summation Notation

4. A series is the sum of the terms in a sequence.
= 135
= 135

5. Find the sum of the first 10 numbers in this sequence. We call it S10!
2, 5, 8, 11, 14, 17, 20
Great! Now find S506!

6. a1•(1 – rn) n ________ Sn = – (a1 + an) 2 Sn = (1 – r) Series Formulas
Arithmetic Series
Geometric Series n 2
a1•(1 – rn)
(1 – r)
________
Sn = – (a1 + an)
Sn =

7. Example 1: Which formula to use?
Evaluate a series with the terms 1, 7, 13, 19, 25 for the first 13 terms.

8. Example 2: Arithmetic or Geometric?
Find the sum of the first 10 terms of the geometric series with a1 = 6 and r = 2.

9. Example 3: Which formula do I use?
A philanthropist donates $50 to the SPCA. Each year, he pledges to donate 12 dollars more than the previous year. In 8 years, what is the total amount he will have donated?