Arithmetic Sequences Unit 6 Notes.

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Presentation transcript:

Arithmetic Sequences Unit 6 Notes

Vocabulary

Vocabulary Finite sequence – has a limited number of terms. Infinite sequence – continues without stopping.

What does arithmetic mean? An arithmetic sequence is a list of numbers with a common difference A common difference means you are ADDING OR SUBTRACTING the same amount between each term.

HW: 1-6 Example 1 Determine if the sequence is arithmetic. If so, find the common difference. 1) 2, 5, 8, 11, … 2) -2, 0, 3, 7, … 3) 3, 1, -1, -3, … HW: 1-6

Ex. 2 Using an Explicit Formula Given the explicit formula for an arithmetic sequence find the first five terms and the 35th term Term # Work Term 1 -12 + 2(1) -10 2 -12 + 2(2) -8 3 -12 + 2(3) -6 4 -12 + 2(4) -4 5 -12 + 2(5) -2 35 -12 + 2(35) 58 HW: 7-10

You Try! Write the first five terms and the 21st term given the explicit formula HW: 7-10

Explicit Formula for Arithmetic Sequences YOU NEED TWO THINGS EVERY TIME: d (common difference) (first term) Memorize This One Kids!!! 𝑎 1

Ex.3 Given the first term and the common difference of an arithmetic sequence find the 1st 5 terms and the explicit formula HW: 11-14

You Try! HW: 11-14

Given a term in an arithmetic sequence and the common difference find the explicit formula Solve for first term and then write explicit formula 𝟐𝟓 = 𝒂 𝟏 +(𝟏𝟏−𝟏)(−𝟑) 𝟐𝟓= 𝒂 𝟏 −𝟑𝟎 𝟓𝟓= 𝒂 𝟏 HW: 15-18

Ex.4 Given a term in an arithmetic sequence and the common difference find the explicit formula HW: 15-18

Homework Handout #1-18