Question 1102476: The 5th term in a sequence is 25, and each term is 3 less than the previous term. Write an explicit rule and a recursive rule to describe the sequence.
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! WITHOUT MEMORIZED FORMULAS:
 or 
would be the recursive rule spelled out in
"each term is 3 less than the previous term."
Then  terms after the 5th term, we would have
subtracted from 25 times 3, so
 , which simplifies to
 and to the simplest explicit rule
 .
Your teacher may have in mind a lot of formula memorizing and writing, like
 = common difference.
 is the memorizable recursive rule formula for any arithmetic sequence,
so in this case  ,
or .
For all arithmetic sequences,
 is the memorizable explicit rule for any arithmetic sequence.
For  , with  and , we can find  :
 .
Plugging 
into the memorized , we get explicit rule
 ,
not that simple, but maybe the expected answer.
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