1. Arithmetic Series

2. A series is the expression for the sum of the terms of a sequence. SequenceSeries 6, 9, 12, 15, 186+9+12+15+18 3, 7, 11, 15,...3+7+11+15+...

3. Evaluate the series Ex. 2, 11, 20, 29, 38, 47 2+11+20+29+38+47 = 147 Ex. 100, 125, 150, 175, 200, 225 100+125+150+175+200+225 = 975

4. An arithmetic series is a series whose terms form an arithmetic sequence. We have a formula for evaluating an arithmetic series easily. a1+a2+a3+...+an = (a1+an) n 2 Hint: a1 is the first term in the series an is the last term in the series n is the number of terms in the series

5. Evaluate the series using the formula Ex. 2, 11, 20, 29, 38, 47 ( )(2+47) = 147 Ex. 100, 125, 150, 175, 200, 225 ( )(100+225) = 975 6 2 6 2

6. Another way to write a series is called summation notation. Ʃ is the Greek letter sigma. Ʃ (5n+1) n=1 n=3 explicit formula for the sequence greatest value of n, the number of terms least value of n,usually n=1

7. Write the explicit formula for the series 3+6+9+...for 33 terms. sequencetermn=#of term What do you have to do to n to get the sequence term? 31n=13*1=3 so, 3n 62n=23*2=6 so, 3n 93n=33*3=9, so, 3n

8. Write the summation notation to write the series 3+6+9+...for 33 terms. Ʃ 3n n=1 n=33

9. Use the series Ʃ (5n+1). a. Find the number of terms in the series. b. Find the first and last terms of the series. c. Evaluate the series. n=1 3 Since the values of n go from 1 to 3. There are three terms because n=1, n=2, and n=3. The first term is n=1, so 5(1)+1=6. The last term is n=3, so 5(3)+1=16 1st term = 6 2nd term = 11 3rd term = 16 6+11+16 = 33

10. Using the calculator to evaluate the series. Steps: 1. Select MATH 2. Select 0:summation Ʃ ( 3. Enter the information in 4. Hint ENTER