document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967747>Question 967747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have the following sequence of runtime for an operation: 3, 6, 11, 18, 27, 38,...<BR>\n" );
document.write( "•	List the next 2 elements in the sequence.<BR>\n" );
document.write( "•	Determine the general equation that yields results for any element of the sequence.<BR>\n" );
document.write( "•	What is the runtime for matrix multiplication operations in terms of big-O notation?\r<BR>\n" );
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document.write( "I am really lost on how to do this. Please send help.  SOS.  Thank You<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591545 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=591545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the given series <BR>\n" );
document.write( "3, 6, 11, 18, 27, 38<BR>\n" );
document.write( "first differences between numbers in series<BR>\n" );
document.write( "3, 5, 7, 9, 11<BR>\n" );
document.write( "second differences from first differences is<BR>\n" );
document.write( "2, 2, 2, 2<BR>\n" );
document.write( "we have a geometric series of order 2, that is<BR>\n" );
document.write( "n^2<BR>\n" );
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document.write( "return to original sequence<BR>\n" );
document.write( "3 6 11 18 27 38<BR>\n" );
document.write( "n^2 terms for nth term are<BR>\n" );
document.write( "1 4  9 16 25 36<BR>\n" );
document.write( "differences is are<BR>\n" );
document.write( "2 2  2  2  2  2<BR>\n" );
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document.write( "This must mean that the rule to find any nth term in this sequence is;<BR>\n" );
document.write( "n^2 +2<BR>\n" );
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document.write( "now we can answer the questions<BR>\n" );
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document.write( "1) the next two numbers in the sequence are<BR>\n" );
document.write( "7^2 +2 = 51<BR>\n" );
document.write( "8^2 +2 = 66<BR>\n" );
document.write( "the next two numbers are 49, 66<BR>\n" );
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document.write( "2) n^2 + 2<BR>\n" );
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document.write( "3) take multiplying two n x n matrices, then<BR>\n" );
document.write( "there are n^2 elements in the output matrix, that would require <BR>\n" );
document.write( "n*n^2 = n^3 operations to compute the entire matrix - that is, the <BR>\n" );
document.write( "speed of the most straightforward algorithm is O(n^k), where k = 3.<BR>\n" );
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