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The graph shows the first three terms in a geometric sequence.

(a)   What is the common ratio r? Explain or show how you determined your answer.

(b)   What is the recursive formula for the sequence?

(c)   What is the iterative formula for the sequence?

Show how to use your answer from Part (c) to find the eighth term of the sequence

Guest Dec 12, 2017
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a. We can determine the common ratio by noting that

5 / 2  =  2.5       and

12.5 / 5  = 2.5

So 2.5 is the common ratio

b.  The recursive formula  is given by :

a =   2.5 * an-1 ,   where a1  = 2

c.   The iterative  (explcit)  formula is given by

an  =    2(2.5)n - 1   ,   where n is the nth term

The eighth term  is       2 (2.5)8-1   =  2(2.5)7  = 78125/64  = 120.703125

CPhill  Dec 12, 2017

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