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Ch. 8 – Sequences, Series, and Probability

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1 Ch. 8 – Sequences, Series, and Probability
8.3 – Geometric Sequences

2 Geometric sequences are always of the form an = a1 rn-1
A sequence is geometric if consecutive numbers always have the same common ratio (r). Ex: 2, 4, 8, 16, 32, … has a common ratio of 2 Ex: has a common ratio of -2/3 Geometric sequences are always of the form an = a1 rn-1 r = the common ratio The sequence will be a1, a1r, a1r2, a1r3, …, a1rn-1

3 Ex: Find a formula for the following geometric sequence, then find a9: 5, 15, 45, …
an = a1rn-1 = 5(3)n-1 a9 = 5(3)8 = 32805 Ex: If the 4th term of a geometric sequence is 125 and the 10th term is 125/64, find the 14th term. Think about the relationship between the 10th and 4th terms!

4 The sum of a finite geometric sequence is:
a1 = 1st term being summed n = # terms being summed r = common ratio Ex: Find the sum: n = 8, a1 = 3(0.6) = 1.8, r = 0.6

5 The sum of an infinite geometric sequence is:
If |r| ≥ 1 , the series does not have a sum. Ex: Find the sum: Use the infinite sum formula! To find a1, evaluate for k = 1 a1 = 4(0.6)1-1 = 4(0.6)0 = 4

6 Find the sum of the series.
16 31.97 15.98 .03 19.98

7 1174 1249 6670 2141 7096 The population in Dodge City decreases by 6% yearly. If the population was 1600 in 1875, what was the population in 1880?

8 Find the sum of the series.
10 7.56 7.45 9.45 9.31

9 Find the sum of the infinite series.
65/6 -9 3/2 9 27/2


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