SOLUTION: Given the sequence: 2, 6, 18, 54, …. a. What is the common ratio? b. What is the recursive formula?

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Question 1137520: Given the sequence: 2, 6, 18, 54, ….
a. What is the common ratio?
b. What is the recursive formula?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given the sequence: 2, 6, 18, 54, ….
a. What is the common ratio?
r=6%2F2=3

b. What is the recursive formula?
a%5Bn%5D=a%5B1%5D%2Ar%5E%28n-1%29
a%5B1%5D=2, r=3
a%5Bn%5D=2%2A3%5E%28n-1%29 for n=1,2,3,....

check the formula:
a%5B1%5D=2%2A3%5E%281-1%29=2%2A3%5E0=2%2A1=2
a%5B2%5D=2%2A3%5E%282-1%29=2%2A3%5E1=2%2A3=6
a%5B3%5D=2%2A3%5E%283-1%29=2%2A3%5E2=2%2A9=18
a%5B4%5D=2%2A3%5E%284-1%29=2%2A3%5E3=2%2A27=54