Hello good people! I cannot understand question 6 in the PrepSwift: Sequences II quiz, and the explanation of the solution at all, is there any alternative approach to this question?
81 + nk = 729
You know that this is an “increasing” arithmetic sequence (as you could tell from “k greater than previous term”) so k > 0. It doesn’t make sense to have non-integer nth term either with n > 0 ( it can’t be less than or equal to 0, why?).
Thus, you rewrite above equation as:
nk = 729 - 81 = 648.
where n,k \in \mathbb{Z}^+
It’s clear that once you fix either k or n, the other variable is uniquely determined. Thus, our only task is to count the number of positive divisors 648.
2 Likes
Got it, Thank you so much.