1. 11.2 Arithmetic Series

2. What is a series?  When the terms of a sequence are added, the indicated sum of the terms is called a series.  Example  Sequence 1, 2, 3, 4, 5, 6  Series 1+2+3+4+5+6

3. Sum of an Arithmetic Series

4. Find the sum of the series 7+12+17+22+…+52 n = 10

5. Find the sum of the first 50 positive even integers

6. Aiden did pushups every day in January. He started on January 1 st and increased the number of pushups done each day by 1. He did a total of 1085 pushups for the month. How many pushups did he do on the first day?

7. Find the first three terms a 1 = 9 a n = 105 S n = 741  Step 1: plug in to find n  Step 2: plug in to find d  Step 3: use d to find the terms

8. Sigma Notation  Compact form for series  Uses the summation symbol Σ  Greek letter sigma

9. Sigma Notation formula for the sequence Last value of n First value of n

10. Ex: For the sequence 1, 2, 3, 4, 5, 6  a 1 = 1  d = 1 a n = 1 + (n – 1)1 a n = 1 + n – 1 a n = n

11. Find the sum 8 n=1 5-2n

12. Find the sum 150 k=1 11 + 2k