document.write( "Question 1159309: Cannonball Pyramids
\n" ); document.write( "Cannonballs can be stacked to form a pyramid with a triangular
\n" ); document.write( "base. Five of these pyramids are shown below. Find the number
\n" ); document.write( "of cannonballs in the 8th pyramid.
\n" ); document.write( "a1 equals 1
\n" ); document.write( "a2 equals 4
\n" ); document.write( "a3 equals 10
\n" ); document.write( "a4 equals 20
\n" ); document.write( "a5 equals 35 \n" ); document.write( "
Algebra.Com's Answer #782322 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "There is no picture of the pyramids.... But we don't need the picture.

\n" ); document.write( "Find the pattern for the given 5 numbers and then continue the pattern to find the 6th, 7th, and 8th numbers.

\n" ); document.write( "The numbers of cannonballs in the pyramids form a sequence of integers. Find the differences between successive terms of the sequence, then the differences between those differences, and so on, until the differences are constant.

\n" ); document.write( "Then you can continue that sequence of constant integers and work backwards to find later terms in the sequence.

\n" ); document.write( "Here is an array showing the terms of the original sequence and the first, second, and third differences:
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document.write( "    1   4  10  20  35\r\n" );
document.write( "      3   6  10  15\r\n" );
document.write( "        3   4   5\r\n" );
document.write( "          1   1

\n" ); document.write( "The third differences are constant. To find three more terms of the sequence, add three more 1's to that row and work backwards up the array of numbers.
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document.write( "    1   4  10  20  35\r\n" );
document.write( "      3   6  10  15\r\n" );
document.write( "        3   4   5\r\n" );
document.write( "          1   1   1   1   1\r\n" );
document.write( "\r\n" );
document.write( "    1   4  10  20  35\r\n" );
document.write( "      3   6  10  15\r\n" );
document.write( "        3   4   5   6   7   8\r\n" );
document.write( "          1   1   1   1   1\r\n" );
document.write( "\r\n" );
document.write( "    1   4  10  20  35\r\n" );
document.write( "      3   6  10  15  21  28  36\r\n" );
document.write( "        3   4   5   6   7   8\r\n" );
document.write( "          1   1   1   1   1\r\n" );
document.write( "\r\n" );
document.write( "    1   4  10  20  35  56  64  100\r\n" );
document.write( "      3   6  10  15  21  28  36\r\n" );
document.write( "        3   4   5   6   7   8\r\n" );
document.write( "          1   1   1   1   1


\n" ); document.write( "The 8th pyramid will have 100 cannonballs.
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