Arithmetic Sequences 3, 7, 11, 15… +4. 3, 7, 11, 15… +4 Common difference is +4. If there is a constant common difference, the sequence is an Arithmetic.

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Presentation transcript:

Arithmetic Sequences 3, 7, 11, 15… +4

3, 7, 11, 15… +4 Common difference is +4. If there is a constant common difference, the sequence is an Arithmetic Sequence.

Ex. #1 Is this an arithmetic sequence? Justify you answer. -4, -2, 0, 2… Ex. #2 Is this an arithmetic sequence? Justify you answer. 1, 4, 9, 25… Ex. #3 Is this an arithmetic sequence? Justify you answer. 9.5, 11.0, 12.5, 14.0… This is an arithmetic sequence because it has a common difference of +2 This is not because there is no common difference. This is an arithmetic sequence because it has a common difference of +1.5.

A sequence can be represented: With a list or table With a verbal description Graphically Algebraically.

Ex. 4 Create a list of four terms from the description given here. The first term, a 1, of the arithmetic sequence is 5 and the common difference, d, is 3. TermsSymbol Representations Value calculated from the description First a1a1 5 Second a2a Third a3a (3) Fourth a4a (3) … nth anan 5 + (n – 1)(3)

The nth value will help us with the algebraic equation. Remember a n = 5 + (n – 1)(3). Simplify… This is an explicit equation for this arithmetic sequence. So the generic formula for an arithmetic sequence is

Looking at the graph of the sequence… What kind of a function would this be if the points were connected? Note: This function starts at one, therefore the domain is n ≥ 1 The term number, n. The actual term

Ex. 5 Write the explicit equation for the nth term for the following sequence and then find the term a 9 21, 17, 13, 9, 5…

Ex. 6 A common difference of an arithmetic sequence is 6 and the a 20 is 121. What is a 1 ?

Ex. 7 The first four terms of an arithmetic sequence are 4½, 7, 9½, and 12. Which term of the sequence is 32?