Question 1196058: Find the general rule/formula of the sequence: 7, 5, 3, ...
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
Without more info, there could be infinitely many possible answers. See my previous post here for more details.
If we assume the sequence is arithmetic, then,
a1 = 7 = first term
d = -2 = common difference
And furthermore,
nth term = a1 + d(n-1)
nth term = 7 + (-2)(n-1)
nth term = 7 -2(n-1)
nth term = 7 -2n+2
nth term = -2n+9
Again this all hinges on the assumption we have an arithmetic sequence.
Answer by ikleyn(52805)  (Show Source):
You can put this solution on YOUR website! .
Another possible rule is to say that the given sequence lists 3 consecutive prime numbers in the descending order.
Then the expected next (and the last) term is 2.
Yet another possible formula is  =  , n = 1, 2, 3, 4, 5, . . .
which gives the sequence repeating cyclically 7, 5, 3, 5, 7, 5, 3, 5 . . .
Yet another formula is = 7 - 2*(n-1) + (n-1)*(n-2)*(n-3)*F(n),
where F(n) is an arbitrary polynomial with integer coefficients.
It produces the same three values at n = 1,2,3, but gives totally different values at n > 3.
I write it to explain you that more than one million possible "rules" and "formulas" can be created.
And without a context or additional info, you do not know and can not know, which is right and what to select.
So, mathematically, the problem and the question are quite non-sensical.
For a mathematically educated person, it is very important to understand it clearly.
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