1. Welcome Activity
1. Find the sum of the following sequence: Find the number of terms (n) in the following sequence: 5, 9, 13, 17, … 81, 85

2. HW Key

3. Summation Notation & Arithmetic Series
Unit 1 Chapter 11
Summation Notation & Arithmetic Series

4. Objectives
Students will be able to find the partial sum of an arithmetic series.
HW: p. 780: 30, 32, 38, 50, 60

5. A series is formed when the terms of a sequence are added.
In general, the sum of n terms in a finite series is written
u1 + u2 + u un = Sn
The sum of an infinite series is written:
u1 + u2 + u = S∞

6. This sum can be expressed using a shorthand notation:
u1 + u2 + u un = Sn =
u1 + u2 + u = S∞ =
Please note that i in this context does not refer to imaginary numbers.

7. Ex 1: Find the sum of the series.

8. Ex 2: Write the series in summation notation.

9. When the famous mathematician Karl Friedrich Gauss ( ) was nine years old, his teacher asked the class to find the sum of the numbers from 1 to Historical accounts indicate the teacher was hoping to take a break from his students and expected the students to add the terms one by one.

10. = S100
= S100
= 2 (S100)

11. Gauss’ creative thinking can be used to derive the explicit formula for the sum of an arithmetic series:
u u u u n u n u n = Sn
u n + u n u n u u u1 = Sn
(u1 + u n ) · n = 2 (Sn)

12. Explicit Formula for the sum of an arithmetic series:
where n is the number of terms,
u1 is the first term, and
un is the last term.

13. Ex 3: Find the sum of the first 10 terms given:
a3 = 5 and a4 = 8.

14. Ex 4: Find the sum of the first 50 multiples of 6.

15. Ex 5: Find a1 and d given S20 = 1090 and a20 = 102

16. Ex 6: Find the sum of the arithmetic series:

17. Ex 7: Evaluate the sum: