Arithmetic Series: {1, 2, 3, 4, … , 100} 1. What type of sequence does the above set of numbers represent? 2. What could be a formula that predicts each term in the sequence? 3. Sum up all the numbers in the sequence Series: expression for the sum of all terms of a sequence If the sequence is infinite then the series is infinite as well. Example: Infinite Sequence: {3, 7, 11, 15, …} Infinite Series: {3+7+11+15+…} Notice – these examples are both arithmetic sequences and therefore are If the sequence is finite, then the series is finite too. arithmetic series. Example: Finite Sequence: {6, 9, 12, 15, 18} Finite Sequence: {6+9+12+15+18} Formula for a FINITE arithmetic series: n
Sn = a1 + an
2
Example: An auditorium has 40 seats in the first row. Every row afterward has €previous. If there are twenty rows to the two more seats than the auditorium, how many total seats does the auditorium have? {40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78} n
20
 Sn = ( a1 + an ) S20 = ( 40 + 78)  Sn = 1180 2
2
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Sigma: This is Sigma. The Greek letter Sigma can be used to replace Sn (the sum of a series) ∑
BUT… Sigma needs some direction What €
Sigma needs: A place to start A place to end A formula that tells Sigma what to add 20
38 + 2n
Upper limit, greatest value of n…the place n =1
to end € Lower limit, the least value of n…the place to start ∑(
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A formula representing the sequence. In this case, this is the formula for the previous auditorium example.