# Complete the number-sequence

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.

• I dont understand the reasons for the downvote. Please explain. Jun 9 '15 at 6:09
• 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. Jun 9 '15 at 10:14

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

• 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. Jun 8 '15 at 3:33
• Thanks. Was trying to fix it while you were doing it too. Jun 8 '15 at 3:34

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.

• 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. Jun 8 '15 at 11:02

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.

• 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) ? Jun 8 '15 at 4:00
• @DippedBits Closed-form formula vs. recursive formula. They're equivalent but still different in a way. Jun 8 '15 at 9:36