Arithmetic Sequences and Geometric Sequences Arithmetic Sequences An









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Arithmetic Sequences and Geometric Sequences

Arithmetic Sequences • An arithmetic sequence is a set of numbers put into a specific order by a pattern of addition or subtraction. • an = a 1 + (n – 1)d– This is the formula. • an represents the nth term, the unknown term that you are trying to find, of a sequence. • a 1 is the first term in a sequence. • n is an unknown term that is always the same number as the n term in an.

Arithmetic Sequences (continued) • The d in the formula is the an=a 1+(n-1)d Common Difference between each of the terms in a series. • For example: 1, 5, 9, 13… The common difference (d) is +4. • The d term can also be negative: 10, 7, 4, 1, -2… The d term is -3 (this means that instead of adding a number you subtract it. )

Geometric Sequences • an = a 1 rn-1 Geometric Sequence formula. • an is the unknown term (just like the arithmetic sequences) • a 1 is the first term. • r is the rate, also known as the common ratio. It is the change between two terms in a geometric sequence. It is either a number being multiplied or divided. You can also multiply by (1) over the number being multiplied.

More Geometric Sequences • Some examples of geometric sequences are: • 1, 2, 4, 8, 16, 32…-- r = 2 • 100, 50, 25, 12. 5, 6. 25…-- r = 1/2 (divide the preceding number by 2. ) an=a 1 rn-1

Some Interesting Example Equations Geometric example: find the nth term. a 1 = -10, r=4, n=2 an = -10(4)2 -1 an = -10(4)1 an = -40 Arithmetic example: find a 14, a 1=4, d=6 a 14= 4 + (14 -1)6 a 14= 4 + 78 a 14= 82

How this relates to Real Life Outside Math Class • A painter is a job that requires the use of an arithmetic sequence to correctly space things he is painting. If the painter was painting stripes on a wall, he could find the places to put the stripes to evenly space them.

Another Real Life Slide • If an owner of a store needed to count up the amount of stuff they sell, or how much money they make, he could use and arithmetic or geometric sequence. • If the owner had a pattern of how much money they make as time progresses, that is a sequence. The owner also needs these sequences if he/she wants to predict the earnings of his or her store in years to come.

Arithmetic and geometric sequences and series
Geometric and arithmetic sequences formulas
Geometric series formula
Recursive and explicit formulas
Geometric progression formula
Lesson 3: arithmetic and geometric sequences
Sequences and series
Geometric sequence
Arithmetic sequence division
Recursive formula geometric