Question 1179832: If f(1)=3 and f(n)=−4f(n−1) then find the value of f(5).
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
If f(1)=3 and f(n)=−4f(n−1) then find the value of f(5).
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f(2) = according to the formula = -4*f(1) = -4*3 = - 12.
f(3) = -4*f(2) = -4*(-12) = 48.
f(4) = -4*f(3) = -4*48 = -192.
f(5) = -4*f(4) = -4*(-192) = 768. ANSWER
The problem is just solved and the answer is obtained, so the assignment is completed.
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For your better understanding, you must learn two things.
One thing is that you have a recursive (or recurrent) formula, so you can move forward, using it, as far as you want.
Each next step is easy and uses the values, that you just obtained in your previous steps.
The other thing is that this simple recursive formula determines nothing else as the GEOMETRIC progression.
By knowing it, you may wright the EXPLICIT formula for the n-th term:
f(n) =  .
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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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Answer by MathLover1(20850)  (Show Source):
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