Question 1196635
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<font color=red>Answer:</font> *[tex \Large a_{n} = (a_{n-1}) + 4]


An equivalent answer would be *[tex \Large a_{n+1} = (a_{n}) + 4]


The first term is *[tex \Large a_{1} = 4]


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 *[tex \large a_{n}] 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 *[tex \large a_{n-1}]


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
*[tex \Large a_{n+1} = (a_{n}) + 4]
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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