LT: I can evaluate Arithmetic and Geometric Series. Warm-Up  

Arithmetic and Geometric Series LT: I can evaluate Arithmetic and Geometric Series. Arithmetic and Geometric Series

LT: I can evaluate 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 LT: I can evaluate Arithmetic and Geometric 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 LT: I can evaluate Arithmetic and Geometric Series. 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 LT: I can evaluate Arithmetic and Geometric Series. WARNING: you MUST have a Geometric Series to use this formula an = a1 * r (n-1)

LT: I can evaluate Arithmetic and Geometric Series. 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… LT: I can evaluate Arithmetic and Geometric Series. Another Way to Write it…  

But what if our series doesn’t start at 1? LT: I can evaluate Arithmetic and Geometric Series. But what if our series doesn’t start at 1?     This would be done the same way for geometric series, but with the geometric formula

LT: I can evaluate Arithmetic and Geometric Series. 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

LT: I can evaluate Arithmetic and Geometric Series. Closure