SOLUTION: 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

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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(20056)   (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(52787)   (Show Source): You can put this solution on YOUR website!
.
On geometric progressions,  see introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

Save the link to this textbook together with its description

Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson

into your archive and use when it is needed.


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