Arithmetic Sequences and Geometric Sequences

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Arithmetic Sequences and Geometric Sequences
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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.

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Arithmetic Sequences (continued)
ana1(n-1)d

• 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.)

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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.

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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.)

ana1rn-1
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Some Interesting Example Equations

• Geometric example find the nth term.
• a1 -10, r4, n2
• an -10(4)2-1
• an -10(4)1
• an -40
• Arithmetic example find a14, a14, d6
• a14 4 (14-1)6
• a14 4 78 a14 82

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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.

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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.

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Finished!