document.write( "Question 155130: I need to know what number comes next in this sequence and why.
\n" ); document.write( "9,73,241,561,1081,1849,_?__
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Algebra.Com's Answer #614181 by terryriegel(1)\"\" \"About 
You can put this solution on YOUR website!

It can be any number you want.

The solution arises from the fact that anything times zero is just zero and also adding zero to something doesn't change it.

Now granted the formula will get a bit lengthy but it is a valid solution and it can be any number you want.

Lets start with a simple sequence of three random numbers between (1-10) from random.org I got 6,9,2,_ whats next, Ok back to random.org its came up with 5.

So our problem is to come up with a formula f(n) that produces f(1)=6, f(2)=9, f(3)=2, and f(4)=5


\n" ); document.write( "f(1)=6
\n" ); document.write( "f(2)=9
\n" ); document.write( "f(3)=2
\n" ); document.write( "f(4)=5

Lets initially choose

f(n) = 6

f(1) = 6 check
\n" ); document.write( "f(2) = 6 fail

so lets refine it

f(n) = 6 + (n-1)(3/1)

f(1) = 6 check
\n" ); document.write( "f(2) = 9 check
\n" ); document.write( "f(3) = 12 fail

so we refine further

f(n) = 6 + (n-1)(3/1) + (n-1)(n-2)(-10/2)

f(1) = 6 check
\n" ); document.write( "f(2) = 9 check
\n" ); document.write( "f(3) = 2 check
\n" ); document.write( "f(4) = -15 fail

so we refine further

f(n) = 6 + (n-1)(3/1) + (n-1)(n-2)(-10/2) + (n-1)(n-2)(n-3)(10/3)

f(1) = 6 check
\n" ); document.write( "f(2) = 9 check
\n" ); document.write( "f(3) = 2 check
\n" ); document.write( "f(4) = 5 check

So to answer the original question using the same methods the formula looks like this...

f(7) = 0

simplified...

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