Warm Up State the pattern for each step.

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Presentation transcript:

Warm Up State the pattern for each step. 3, 6, 12, 24, 48, 96,… 81, 27, 9, 3, 1, ⅓,… -2, 4, -8, 16, -32, 64, -128

Geometric Sequences

An geometric sequence is a sequence of numbers with a common ratio.

Is the given sequence geometric? If so, identify the common ratio. 5, 15, 45, 135, … 15, 30, 45, 60, … 6, -24, 96, -384, … 8, 20, 32, 44, … 1, 2, 4, 8, … 7, 0.7, 0.07, 0.007, … 10, 4, 1.6, 0.64, …

an = a1 • r (n-1) Geometric Sequence Formula 1st term If you are solving for a16, just write 16 here 1st term an = a1 • r (n-1) common ratio nth term. For example, the 16th term would be a16

Example 1: an = a1 • r (n-1) Given the sequence 4, 28, 196, 1372, 9604,…, find the value of the 14th term.

Example 2: an = a1 • r (n-1) Given the sequence -2, 6, -18, 54, -162,…, find the value of the 17th term.

Example 3: an = a1 • r (n-1) Given the sequence 100, 83, 68.89, 57.1787,…, find the value of the 9th term.

Example 4: an = a1 • r (n-1) Given the sequence 1, 5, 25, 125, 625, 3125,…, find the term number that has a value of 9,765,625.

Example 5: an = a1 • r (n-1) Suppose you want a reduced copy of a photograph. The actual length of the photograph is 10 in. The smallest size the copier can make is 64% of the original. Find the length of the photograph after five reductions.

Geometric Mean Used to find the missing term of a geometric sequence The positive square root of the product of the two numbers

Geometric Mean Ex 10: Find the missing term of each geometric sequence 20, ____, 80, … 3, ____, 18.75, … 28, ____, 5103, …