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Bellwork:. Determine whether each of the following is Arithmetic (something was added each time), Geometric ( something was multiplied each time), or Neither -2, -4, -8, -16… 10, 0, -10, -20… 4, 9, 16, 25…. Notation: .

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Bellwork:

  • Determine whether each of the following is Arithmetic (something was added each time), Geometric (something was multiplied each time), or Neither

  • -2, -4, -8, -16…

  • 10, 0, -10, -20…

  • 4, 9, 16, 25…


Notation:

  • d= common difference (what is added to each term of an arithmetic sequence)

  • r= common ratio (what is multiplied to each term of a geometric sequence)

  • n= What term number you are looking at (4th term, 10th term… nth term)


How to find the nth term of an arithmetic sequence

The Formula:

Common Difference

nth term

First term


How to find the nth term of an arithmetic sequence

EX: -14, -5, 4, 13, …

becomes


How to find the nth term of an arithmetic sequence

Simplify…


How do we find the 30th term of an arithmetic sequence?

Just plug in 30 for n!


How to find the nth term of a geometric sequence.

The Formula:

Common Ratio

nth term

First term


How to find the nth term of a geometric sequence.

EX: 4, 20, 100, 500, …

becomes


How do we find the 10th term of an geometric sequence?

Just plug in 30 for n!


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