1. Grade 11 Functions (MCR3U)
Unit 5: Pascal’s Triangle, Binomial Theorem, Sequences & Series Geometric Sequences
Mr. Choi
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2. Geometric Sequence {a, ar, ar 2, ar 3,...}
A sequence like 3, 9, 27, 81,…, where the ratio between consecutive terms is a constant, is called a geometric sequence. In a geometric sequence, the first term t1, is denoted as a. Each term after the first is found by multiplying a constant, called the common ratio, r, to the preceding term.
The list then becomes .
{a, ar, ar 2, ar 3,...}
Geometric Sequences
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3. Geometric Sequences Formulas
In general: {a, ar, ar 2, ar 3,...,ar n-1 ,...}
Geometric Sequences
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4. Example 1 – Finding Formula for the nth term
In the geometric sequences: {5, 15, 45,...}, find a) b) c) c) b) a) 10 n 10 n n n 5 5
Geometric Sequences
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5. Example 2 – Finding Formula for the nth term
Given the geometric sequence: {3, 6, 12, 24, ...}.
Find the term
Which term is 384?
We know the nth term is 384 !! b) a) n n 14 14
Drop the bases!!
Geometric Sequences
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6. Example 3 – Find the terms in the sequence
In a geometric sequence, t3 = 20 and t6 = Find the first 6 terms of the sequence.
(2) (1)
Substitute into (1)
(1)
(2)
Therefore the first 6 terms of the sequences are:
Geometric Sequences
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7. Example 4 – Find the terms in the sequence
In a geometric sequence, t3 = 20 and t6 = Find the first 6 terms of the sequence. METHOD 2
To find a, we use the same thinking process!!
t1 = 20r(1-3)
tn=20r (n-3)
Therefore the first 6 terms of the sequences are:
Geometric Sequences
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8. Example 5 – Applications of Geometric sequence
Determine the value of x such that
Form a geometric sequence. Find the sequences and
Therefore the sequences are:
5+4, 2(5)+5, 4(5)+5, ...
9, 15, 25,...
Geometric Sequences
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9. Homework: Text Book: P. 392 #1,2bcefh,3-4,5bcdf,6-9,11,14-20
Work Sheet:
Geometric Sequences
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Geometric Sequences
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10. End of Lesson Geometric Sequences
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