11.5 Arithmetic and Geometric Series

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Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?

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Presentation transcript:

11.5 Arithmetic and Geometric Series

Sum of the first n terms of Arithmetic Series n = # of terms t1 = 1st term tn = nth term Ex) Find the sum of the first 40 terms (S40) of the Arithmetic Series: 2 + 5 + 8 + 11 + … Find the 40th term: t1 = 2 d = 3 Find the sum:

Ex) Evaluate First expand the series to get t1 and t20: (5(1)+2) + … + (5(20)+2) 7 + … + 102 Find S20:

Sum of first n terms of Geometric Series (new formula) n = # of terms t1 = 1st term r = common ratio Ex) Evaluate: Expand: (don’t need last term in geo, yay!) + … 3 + … t1 = 3 n = 10 Find r: r

Sum of first n terms of Geometric Series n = # of terms t1 = 1st term r = common ratio t1 = 3 n = 10 r = -2 exponents first!!

YOYO- find S9 for the Geo. Series with Clue: It’s a BIG number t1 = 5 r = -3

A Partial Sum is given, find n. Arithmetic Series, Sn = 4859, t1=8 d = 5 Find n (Need Quad. Formula for Arith)

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Homework Pg. 587-588 Q1-10, 1 – 31 odd