document.write( "Question 1072844: what is the number sequence or pattern for 0, 1, 8, 27, 64 .... \n" ); document.write( "

Algebra.Com's Answer #687693 by rothauserc(4718) $\"\"$ $\"About$

You can put this solution on YOUR website!
The solution is
\n" ); document.write( ":
\n" ); document.write( "a(n) = n^3 where a(n) is the nth term
\n" ); document.write( ":
\n" ); document.write( "we determine this by using the difference approach
\n" ); document.write( ":
\n" ); document.write( "0, 1, 8, 27, 64
\n" ); document.write( ":
\n" ); document.write( "level one differences between terms is
\n" ); document.write( ":
\n" ); document.write( "1, 7, 19, 37
\n" ); document.write( ":
\n" ); document.write( "level 2 differences between level 1 differences is
\n" ); document.write( ":
\n" ); document.write( "6, 12, 18
\n" ); document.write( ":
\n" ); document.write( "level 3 differences between level 2 differences is
\n" ); document.write( ":
\n" ); document.write( "6, 6
\n" ); document.write( ":
\n" ); document.write( "the level 3 differences are the same so we know we have a n^3 term
\n" ); document.write( ":
\n" ); document.write( "n^3 term gives us 0, 1, 8, 27, 64 so we are done
\n" ); document.write( ":
\n" ); document.write( "Note that in some cases it may be necessary to add or subtract a constant as well as multiply the exponent term by a constant
\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "

\n" );