- Slides: 9
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.