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
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 :
an = 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