SOLUTION: 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.

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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