Transcript Arithmetic Sequences and Geometric Sequences

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 = a1 + (n – 1)d– This is the formula.
• an represents the nth term, the unknown term
that you are trying to find, of a sequence.
• a1 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
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 = a1rn-1 Geometric Sequence formula.
• an is the unknown term (just like the arithmetic
sequences)
• a1 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=a1rn-1
Some Interesting Example
Equations
Geometric example: find the nth term.
a1 = -10, r=4, n=2
an = -10(4)2-1
an = -10(4)1
an = -40
Arithmetic example: find a14, a1=4, d=6
a14= 4 + (14-1)6
a14= 4 + 78
a14= 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
the 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.