of 36/36
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

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

• View
215

1

Embed Size (px)

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

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

Documents
Documents
Documents
Documents
Education
Documents
Documents
Documents
Education
Documents
Documents
Technology
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Documents
Education
Documents
Documents
Documents
Documents
Documents
Documents
Documents