2 → 6
3 → 12
4 → 20
5 → 30
6 → 42
9 → ?
Can you find a correspondence between these numbers?
It's not mine, so I don't take any credit. I've just seen it in Linkedin and wanted to share with the community.
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1$\begingroup$ I dont understand the reasons for the downvote. Please explain. $\endgroup$– David SánchezCommented Jun 9, 2015 at 6:09
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$\begingroup$ I deleted my other comment because I actually gave away the answer. I am not one of the down voters, but I would attribute them to this being a low quality question that was copied from Facebook where a large amount of people have seen it. It is also a trivial math question for people who frequent this site. $\endgroup$– LeppyR64Commented Jun 9, 2015 at 10:14
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3 Answers
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90
Reasoning:
f(n) = n * (n+1)
Thus,
2 * 3 = 6,
3 * 4 = 12,
4 * 5 = 20,
5 * 6 = 30,
6 * 7 = 42,
9 * 10 = 90
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1$\begingroup$ I've fixed up your formatting that I saw you were trying to get working - for future reference, put two spaces at the end of a paragraph to make sure it moves to the next line, and an exclamation mark after each ">" to maintain the spoiler text. Then check that it's right before accepting the edit. $\endgroup$– Glen OCommented Jun 8, 2015 at 3:33
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$\begingroup$ Thanks. Was trying to fix it while you were doing it too. $\endgroup$ Commented Jun 8, 2015 at 3:34
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I think you guys are overthinking this one. I'm a simple guy, with a simple answer (albeit the same).
90
The sequence:
2 * 3 = 6
3 * 4 = 12
4 * 5 = 20
5 * 6 = 30
6 * 7 = 42
7 * 8 = 56
8 * 9 = 72
9 * 10 = 90
Basically, the pattern follows each successive number. Or, in simpler terms, once you've figured out the math behind the original question, you just add +1 to each side of the multiplication sign until you reach the final answer.
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$\begingroup$ Why the down vote? I just gave a simple way to answer it as well. I don't understand formulas well so this is the way my brain interpreted it. $\endgroup$ Commented Jun 8, 2015 at 11:02
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Obviously, this follows the pattern $b_n=2n +b_{n-1}$ for $n\in\{3,4,5,6\}$, with $b_2=6$. Assuming the pattern continues for $n\in\{7,8,9\}$, we get $b_9=2(9)+b_8=18+2(8)+b_7=34+2(7)+b_6=48+42=90$.
There are, of course, other answers, of which I will show later.
This is another possible solution:
If this is of the form $a_n = b_n, a_n ∈ A. b_n ∈ B$): $A = \{2,3,4,5,6,9\}$ and $B = \{x_n ∈ A : x_nx_{n-1}\}$. Since $a_n = b_n$, we must find $a_6$, which is $b_6$. $b_6 = a_6a_5 = 9(6) = 54$.
I thus also conclude $9 = 54$.
(As a side note, using the "equality" sign to represent some function sort of rubs me the wrong way, as it has a long-standing representation. I do like how here (as opposed to how I originally saw it), the ‘→’ is used instead. Kudos!)
See here for a discussion, from which I drew my former answer (from myself). The former solution was just another way of tackling the common answer, also from myself.
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1$\begingroup$ How is your solution different than the one I gave? Your function boils down to the same function. f(n) = 2n + f(n-1) = 2((n*(n+1)/2) = n * (n+1) ? $\endgroup$ Commented Jun 8, 2015 at 4:00
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$\begingroup$ @DippedBits Closed-form formula vs. recursive formula. They're equivalent but still different in a way. $\endgroup$ Commented Jun 8, 2015 at 9:36