Question 1136792: The sequence 2, 6, 18, 54, ... is geometric. Find
(1) the common ratio,
(2) the ninth term,
(3) a recursive rule for the nth term, and
(4) an explicit rule for the nth term
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website! The sequence 2, 6, 18, 54, ... is geometric. Find
(1) the common ratio,
Since they are all the same, that shows that the sequence is
geometric, and that the common ratio, r=3.
(2) the ninth term,
2, 6, 18, 54, 54∙3=162, 162∙3=486, 486∙3=1458, 1458∙3=4374, 4374∙3=13122
(3) a recursive rule for the nth term,
a1 = 2, an+1 = 3∙an for n≥1.
(4) an explicit rule for the nth term
an = a1∙rn-1
an = 2∙3n-1
Edwin
Answer by ikleyn(52903)  (Show Source):
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