SOLUTION: 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 th

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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(52832)   (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.


------------------


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:

An equivalent answer would be

The first term is

n is a positive integer.

-----------------------------------------------------------------------------
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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