Question 1180309: The second term of an exponential sequence is 9 while the fourth term is 81. Find the common ratio and first term
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
The second term of an exponential sequence is 9 while the fourth term is 81.
Find the common ratio and first term
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Then the ratio  is  , where r is the common ratio.
So, r^2 = 9, which implies r =  = +/- 3.
Thus for r we have two possible answers, the values 3 and -3.
If r = 3, then the first term is  = 9/3 = 3.
If r = -3, then the first term is = 9/(-3) = -3.
ANSWER. There are two solutions: a) r= 3, = 3, and b) r= -3, = -3.
Solved.
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Standard name/term for the exponential sequence is a Geometric progression/sequence.
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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