WEBVTT
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[MUSIC PLAYING]
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MICHAEL ANDERSON: Geometric sequences
are similar to arithmetic
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sequences.
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But instead of there
being a common difference,
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the amount that is added on each
time, there is a common ratio--
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a common amount we multiply
by to get from one term
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to the next.
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A simple geometric sequence
is the powers of 2.
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In this case, g equals 2,
4, 8, 16, and 32, and so on.
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Just like arithmetic sequences
are based upon the times
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tables, geometric sequences
are based upon power sequences.
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G is equal to 2 to the power
of 1, 2 to the power 2,
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2 to power 3, 2 to the power
4, 2 to the power 5, and so on.
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The first term is 2.
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And the common ratio--
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the number that we
multiply the previous term
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by to get the next
term is also 2.
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We can express the
term-to-term rule
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as G1, the first term
being equal to 2.
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And to get the next term, we
multiply the current term by 2.
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The position to term rule
is 2 to the power of n.
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We can find the common ratio
in a geometric sequence
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by dividing the current
term by the previous term.
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That will give us
r, the common ratio.
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In a geometric sequence, we
can find the common ratio r
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by dividing the current
term by the previous term.
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An example of a similar
geometric sequence
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is H. H is equal to 6,
12, 24, 48, 96, and so on.
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This is still a
geometric sequence.
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We can find the common
ratio by dividing
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one term by the previous term.
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For example, 24
divided by 12 equals 2.
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Or 96 divided by
48 also gives us 2.
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The common ratio
r is equal to 2.
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We can describe the
term-to-term rule like this.
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H 1, our first term is 6.
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To get the next term, we
multiply the current term by 2.
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Let's have a look at the
position to term rule.
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H is based on the number
sequence, 2 to the power n.
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In this case, the sequence is
always 3 times the value of 2n.
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So H n is equal to 3
multiplied by 2 to the power n.
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Let's look at another example.
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J is equal to 4, 8,
16, 32, 64, and so on.
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We can describe the sequence
using a term-to-term rule.
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J1, the first term, is 4.
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And we get the next term by
multiplying the previous term
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by 2.
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We can write the position to
term rule as Jn is equal to 2
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to the power of n plus 1.
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The position to term rule
can be found by multiplying 2
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by 2 to the power of n.
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Another way of writing this
is 2 to the power of n plus 1.
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Have a go of writing the first
five terms of the following
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sequences--
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3 to the power of
n, 4 multiplied by 3
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to the power of n, and 3
to the power of n plus 2.
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