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Arithmetic Sequences

Arithmetic Sequences. 3, 7, 11, 15…. +4. +4. +4. 3, 7, 11, 15…. Common difference is +4. If there is a constant common difference, the sequence is an Arithmetic Sequence. +4. +4. +4. Ex. #1 Is this an arithmetic sequence? Justify you answer. -4, -2, 0, 2….

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Arithmetic Sequences

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  1. Arithmetic Sequences 3, 7, 11, 15… +4 +4 +4

  2. 3, 7, 11, 15… Common difference is +4. If there is a constant common difference, the sequence is an Arithmetic Sequence. +4 +4 +4

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

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

  5. Ex. 4 Create a list of four terms from the description given here. The first term, a1, of the arithmetic sequence is 5 and the common difference, d, is 3.

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

  7. Looking at the graph of the sequence… What kind of a function would this be if the points were connected? 14 12 10 The actual term 8 6 4 2 Note: This function starts at one, therefore the domain is n ≥ 1 1 2 3 4 The term number, n.

  8. Ex. 5 Write the explicit equation for the nth term for the following sequence and then find the term a9 21, 17, 13, 9, 5…

  9. Ex. 6 A common difference of an arithmetic sequence is 6 and the a20 is 121. What is a1?

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

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