11.2 Arithmetic Series. What is a series?  When the terms of a sequence are added, the indicated sum of the terms is called a series.  Example  Sequence.

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11.2 Arithmetic Series

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

Sum of an Arithmetic Series

Find the sum of the series …+52 n = 10

Find the sum of the first 50 positive even integers

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?

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

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

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

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

Find the sum 8 n=1 5-2n

Find the sum 150 k= k