document.write( "Question 1150514: Clara organizes cans in triangular piles, where each row has one less can than the row below. For example, the pile of 15 cans has 5 cans in the bottom row and 4 cans in the row above it.\r
\n" ); document.write( "\n" ); document.write( "(a) There are 3240 cans in a pile. How many cans are in the bottom row?\r
\n" ); document.write( "\n" ); document.write( "(b) There are S cans and they are organized in a triangular pile with 'n' cans in the bottom row. Show that n^2 +n - 2S= 0\r
\n" ); document.write( "\n" ); document.write( "(c) Clara has 2100 cans. Explain why she cant organize them in a triangular pile. \n" ); document.write( "
Algebra.Com's Answer #771948 by htmentor(1343)\"\" \"About 
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a) This problem involves an arithmetic sequence with common difference of -1, and the last term equal to 1.
\n" ); document.write( "The nth term of an arithmetic sequence is a_n = a_1 + (n-1)d
\n" ); document.write( "So we have 1 = a_1 + (1-n)
\n" ); document.write( "Thus a_1 = n
\n" ); document.write( "The sum of an arithmetic sequence with n terms is
\n" ); document.write( "S_n = (n/2)(a_1 + a_n)
\n" ); document.write( "6480 = a_1^2 + a_1
\n" ); document.write( "The solutions are a_1 = 80, -81
\n" ); document.write( "Take the positive solution, a_1 = 80
\n" ); document.write( "b) The above equation can be written 2S = n((n + 1) -> n^2 + n - 2S = 0
\n" ); document.write( "c) n^2 + n - 2*2100 = 0
\n" ); document.write( "n^2 + n - 4200 = 0
\n" ); document.write( "There are no integer solutions, thus this number of cans cannot be made into a triangular pile \n" ); document.write( "
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