Arithmetic and Geometric Series Sequence vs Series Sequence

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 = a 1 + (n – 1)d

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

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

Example Sn = a 1 (1 – rn) 1–r • Find the sum of the first ten terms of the geometric series 16, – 48, 144, – 432, … n = 10 a 1 = 16 r = -3 S 10 = 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? 3 rd 3 3 3 16 16 24 48 48 212 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