Warmup Solve the following systems of equations by the method of your choice: 1) 2)

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Presentation transcript:

Warmup Solve the following systems of equations by the method of your choice: 1) 2)

What are partial sums of arithmetic sequences related to? Acc. Alg/Geom A UNIT QUESTION: How is a geometric sequence like an exponential function? Standard: MM2A2, MM2A3 Today’s Question: What are partial sums of arithmetic sequences related to? Standard: MM2A3d

Arithmetic Sequences & Series

Arithmetic Sequence

Arithmetic Sequence An arithmetic sequence is a list of numbers that are all separated by a common difference. The sequence, and any specific term in it, can be generated using the formula

the nth term the first term the common difference the number of the term you seek (i.e., if you want the 4th term, use a 4)

Let’s try it out: 7, 11, 15, 19, 23, …… What is the formula for this sequence? What is the 213th term?

Let’s try it out: 25, 17, 9, 1, -7, …… What is the formula for this sequence? What is the 137th term?

Let’s try it out: -12, -7, -2, 3, 8, …… What is the formula for this sequence? What is the 384th term?

Let’s try it out: What is the formula for this sequence? What is the 36th term?

Arithmetic Series

Arithmetic Series Series: sum of the terms of part of a sequence Can be written in sigma notation form Two methods: Finding all terms & adding them Formula

Finding all terms and adding Find the sum of the first 7 terms

Find the sum of the first 7 terms Using a formula Find the sum of the first 7 terms

Sigma Notation Discuss what each part of the notation means…

Find the sum of the first 50 terms Have students find the sum using formula. Discuss why it’s so small (sequence is decreasing). How would this be written in sigma notation? What is the total?

Solve

Solve Cannot use the formula

Mixed Practice worksheet Homework Mixed Practice worksheet