Geometric Sequences and Series

Apr 14th, 2015
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After an explanation of the formulas to be used, the practice begins with finding the common ratio and then moves on to the application of finding next four terms. Increasing in difficulty, three or four geometric means have to be calculated. The final questions deal with the sum of a geometric series and the sum of an infinite number of geometric terms. A thorough revision, guide and examination practice.

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Geometric Sequences and Series Reminder : 1. In a geometric sequence the ratio of any term to the preceding term is a constant (called the common ratio, r): tn/tn-1 = r2. The formula for the nth term of a geometric sequence is: Un = U1 r ^ (n-1) = a rn-1 where the first term is a, and common ratio r3. The formula for the Sum of n terms of a geometric sequence is: Sn = U1 [(r ^ n) -1] = a ( rn -1) where the first term is a, and common ratio r r -1 r -14. The sum of an infinite number of terms of a geometric series : S? = a (-1 < r <1) 1 -rAnswer each of the following problems. Make sure to show your work. 1) What is the common ratio of the following geometric sequence? 5, 15, 45,?2) What are

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