Arithmetic and Geometric Series

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Presentation transcript:

Arithmetic and Geometric Series

Sequence vs. Series Sequence – a set of numbers that follow a general rule Examples: 1, 8, 15, 22, 29, … -8, 2, -1/2, 1/8, … Series – the sum of the terms in a sequence of numbers Examples: 1 + 8 + 15 + 22 + 29 + … -8 + 2 – 1/2 + 1/8 - …

Finite Arithmetic Series WARNING: you MUST have an Arithmetic Series to use this formula Reminder: the formula for an arithmetic sequence is an = a1 + (n – 1)d

Example n = 60 a1 = 9 a60 = ? a60 = 9 + (60 – 1)5 = 304 Find the sum of the first 60 terms in the arithmetic series 9, 14, 19, … n = 60 a1 = 9 a60 = ? an = a1 + (n – 1)d a60 = 9 + (60 – 1)5 = 304 S60 = 60 (9 + 304) 2 = 30 (313) = 9390

Finite Geometric Series WARNING: you MUST have a Geometric Series to use this formula an = a1 * r (n-1)

Example Sn = a1 (1 – rn) 1 – r Find the sum of the first ten terms of the geometric series 16, – 48, 144, – 432,… n = 10 a1 = 16 r = -3 S10 = 16 [1 – (-3)10] 1 – (-3) = 16 (1 – 59,049) 4 = -236,192

Another Way to Write it…

But what if our series doesn’t start at 1? 3rd 3 3 16 3 16 48 212 212 24 48 This would be done the same way for geometric series, but with the geometric formula

Things to remember A sequence is a list of numbers, a series is a sum of that list of numbers You need to know the formulas for arithmetic and geometric sequences and for arithmetic and geometric series (4 formulas) If your series doesn’t start at 1 then you must create a subtraction problem to find the series

Make sure you took notes, did all examples, and answer the questions on the website