Step-by-step explanation:
You are asking if an odd n exist such that taking the sequence n, n+2, n+4, we have that
5*(n+2)^2 = n*(n+4) + 488 eq.
5*(n^2 + 4*n + 4) = n^2 + 4*n + 488 eq.
4*n^2 + 16*n - 468 = 0 eq.
n^2 + 4*n - 117 = 0 eq.
(n + 13)*(n - 9) = 0 eq.
n = -13 OR n = 9. (Both these solutions are odd.)
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Answers & Comments
Step-by-step explanation:
You are asking if an odd n exist such that taking the sequence n, n+2, n+4, we have that
5*(n+2)^2 = n*(n+4) + 488 eq.
5*(n^2 + 4*n + 4) = n^2 + 4*n + 488 eq.
4*n^2 + 16*n - 468 = 0 eq.
n^2 + 4*n - 117 = 0 eq.
(n + 13)*(n - 9) = 0 eq.
n = -13 OR n = 9. (Both these solutions are odd.)