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Homework Questions Arithmetic Series Mrs. Ramsey Arithmetic Series A series is the expression for the SUM of the terms in a sequence. Finite sequences and series have terms you can count individually from 1 to a final whole number, n. Infinite sequences and series continue without end. (infinity) Examples Finite Sequence: 6, 9, 12, 15, 18 Finite Series: 6 + 9 + 12 + 15+ 18 Infinite Sequence: 3, 7, 11, 15… Infinite Series: 3 + 7 + 11 + 15 +… Finite Sequence 2, 11, 20, 29, 38, 47 Write the related series: Evaluate the series: An arithmetic series is a series whose terms form an arithmetic sequence. Sum of a Finite Arithmetic Series: n S (a1 a n ) n 2 a1: 1st term an: nth term n: number of terms Example: Find the sum: 1, 3, 5, 7 DON’T just add…use the formula Sn n (a1 a n ) 2 Summation Notation 3 ( 5 n 1 ) n 1 Write the series in summation notation: 1. 3 + 6 + 9 +…for 33 terms 2. 1 + 2 + 3 + …for n=6 3. 3 + 8 + 13 + 18 +…for n=9 Find the sum of the series: 3 1. (5n 1) n 1 10 2. (n 3) n 1 4 1 ( 3. 2 n 1) n 1 5 4. 2 n n2 Homework WORKSHEET Sticker sheet online – do as many as you want!