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7th Grade Math / Lesson 6: Arithmetic/Geometric Sequence

ARITHMETIC/GEOMETRIC SEQUENCE
What will we be learning in this lesson?


  • In this lesson, you will look at the difference between arithmetic and geometric sequences.

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


ARITHMETIC/GEOMETRIC SEQUENCE


  • A sequence is a set of numbers that follows a pattern.

  • We will look at two types of sequences, Arithmetic and Geometric.

  • Arithmetic sequences are found by adding the same number throughout the sequence.

  • Geometric sequences are found by multiplying the same number throughout the sequence.


ARITHMETIC/GEOMETRIC SEQUENCE


  • To identify if a sequence is arithmetic or geometric (or neither) you need to determine if there is a common number that you can add throughout the sequence (arithmetic), a common number that you can multiply throughout the sequence (geometric), or no common number to add or multiply (neither). 
  • Look at the following. Decide if they are arithmetic or geometric sequences, or neither.
  • 21, 18, 15, 12, ...
  • 1, 4, 16, 64, 256, ...
  • 2, 4, 7, 11, 16, ...
 


ARITHMETIC/GEOMETRIC SEQUENCE


  • Look at the following. Decide if they are arithmetic or geometric sequences, or neither.
  • 21, 18, 15, 12, ...       Arithmetic, add -3 to each term
  • 1, 4, 16, 64, 256, ...    Geometric, multiply each term by 4
  • 2, 4, 7, 11, 16, ...       Neither, no common number to add or multiply
 


ARITHMETIC/GEOMETRIC SEQUENCE


  • Use the given rule to find the first 5 numbers of the sequence.
1.  Start with 1 and multiply by -3 repeatedly.
 
 
2.  Start with 1 and add 6 repeatedly.
 
 
 


ARITHMETIC/GEOMETRIC SEQUENCE


  • Use the given rule to find the first 5 numbers of the sequence.
1.  Start with 1 and multiply by -3 repeatedly.
 
1,  -3,  9,  -27,  81, ...
Each term was multiplied by -3 to get the next number.
 
2.  Start with 1 and add 6 repeatedly.
 
1, 7, 13, 20, 27, ...
Each term was increased by 6 to get the next number.
 
 
 
 


 


  • Can you distinguish between an arithmetic and a geometric sequence?

  • Can you find subsequent terms of a sequence given the rule? Be sure to go back to your classroom to get any homework assignments or other activities you need to attend to.