Question 1196635: The table below shows the length of a side of a square garden and the perimeter of the garden(I already posted this question, but I didn’t include the full question because I thought I could solve that piece myself(also, thank you evatrrr).
Length of side: 1| Perimeter: 4
Length of side: 2| Perimeter: 8
Length of side: 3| Perimeter: 12
Length of side: 4| Perimeter: 16
Length of side: 5| Perimeter: 20
What is the recursive formula for the perimeter of a square of side n(the nth perimeter) using the first number(perimeter) in the pattern?| I am not sure what the answer is, but the answer I got was: an = an(n - 1) + 4
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52824)   (Show Source):
You can put this solution on YOUR website! .
You are not sure what the answer is.
Meanwhile, I myself am not sure what the question is - - - so dark and unclear is its meaning.
When a " problem " comes in such formulation,
it is only good to scare people around - - - not to teach them.
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A normal mathematical formulation, in normal mathematical language, is THIS
Find a recursive formula for sequence 4, 8, 12, 16, 20.
That's all. No more words.
- - - - - To a person who created/composed this " problem ", I'd like to say THIS - - - -
Hey, without knowing musical notations and elementary musical grammar, arpeggio and solfeggio,
would you try to write a music symphony ?
The answer is 129% NO.
Then WHY do you try to compose Math problems, without having adequate knowledge on how to do it ?
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
Answer:  + 4)
An equivalent answer would be  + 4)
The first term is 
n is a positive integer.
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Further Explanation:
The sequence is
4, 8, 12, 16, 20
Each time we need a new term, add on 4
eg: 8+4 = 12
The  represents the nth term, where n is some positive integer from the set {1,2,3,4,5,...}
To find this nth term, we add 4 to the previous term just before the nth term. That previous term being 
This is how we can describe the recursive form in words
nth term = (term just before nth term) + 4
Some textbooks will use this type of notation
a(n) = a(n-1)+4
where a(n) is the nth term and a(n-1) is the term just before the nth term.
Now we could re-index things to say
aka
a(n+1) = a(n)+4
and it means "to find the (n+1)th term, add 4 to the nth term".
So it's up to you which format you prefer better.
Keep in mind that a(n) and a(n-1) and a(n+1) are function notation, and NOT multiplication. We can't use the distribution rule here.
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