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*Geometric Sequences A geometric sequence is a sequence where each # in the seq. is multiplied by a...*

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Geometric Sequences A geometric sequence is a sequence where each # in the seq. is multiplied by a constant (which is called the common ratio (r)) To find r, divide any term in the sequence by the previous term

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Unit 10 Sequences and Series

Geometric SequencesA geometric sequence is a sequence where each # in the seq. is multiplied by a constant (which is called the common ratio (r))

To find r, divide any term in the sequence by the previous termGeometric SequencesGeneral Formula:

Geometric SequencesFind the 11th term of the geo. Sequence listed below

64, -32, 16, -8,a11

Geometric SequencesFind the 6th term of the geo. sequence listed below

3, -15, 75, ..a6

Geometric SequencesWrite an equation for the nth term

3, 12, 48, 192...an

Geometric SequencesFind the 10th term of the sequence if

a4=108r=3

Geometric SequencesFind the 7th term of the sequence if

a3=96r=2

Geometric MeansGeometric means are the missing terms between two non-successive terms in a geo. Sequence

Find 3 geometric means between 2.25 and 576Geometric MeansFind 5 geometric means between and 1/1458Geometric SeriesA series that is associated with a geometric sequence

Geometric SeriesFind the sum of the first 6 terms of the geometric series 3 + 6 + 12 + 24 +

Geometric SeriesFind the first term of the series if the S8=39,360 and r=3

Geometric SeriesFind the sum of the first 8 terms of1+x+x2+x3+

Sigma NotationMore concise (less time consuming) notation for writing out a series

Sigma Notation

Sigma Notation

Sigma Notation

Write in sigma notation1 + 3 + 5 + 7Write in sigma notation2 + 4 + 6 + 8 + 10Write in sigma notation3 + 6 + 12 + 24 + 48Write in sigma notation-3 + 9 + -27 + 81 + -243Write in sigma notation-2 + 4 + -8 + . . . +256Infinite Geometric SeriesIn an infinite series, Sn approaches some limit as n becomes very large. That limit is defined to be the sum of the series. If an infinite series has a sum, it is said to converge.

A series converges (or has a sum) if and only if lrl < 1Does the geom. series have a sum?

Does the geom. series have a sum?

Does the sum of each term approach some limit?To find the sum of an infinite seriesMake sure a limit exists first

An infinite series in sigma notationfind the sum

An infinite series in sigma notationfind the sum

Writing a repeating decimal as a fraction

Writing a repeating decimal as a fraction

A different kind of sequence. . . ExpandPascals Triangle11 11 2 11 3 3 11 4 6 4 11 5 10 10 5 11 6 15 20 15 6 1First row is used for anything to the zero power.Used for the coefficients of each term of the expanded binomialExpand using Pascals Triangle

Expand using Pascals Triangle