document.write( "Question 1202439: Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836. \n" ); document.write( "

Algebra.Com's Answer #837283 by ikleyn(52798) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Calculate the sum of the series: - 396 - 308 - 220 - 132 - ... + 836.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The sequense  -396, -308, -220, -132, . . ., 836  is an arithmetic progression\r\n" );
document.write( "with the first term  a= -396  and the common difference of d= 88  \r\n" );
document.write( "(sinse -308 - (-396) = 88  and each next term is 88 units greater than the current term).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Find the number of term. Use the formula for the n-th term\r\n" );
document.write( "\r\n" );
document.write( "    836 = -396 + 88*(n-1).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives  (836 + 396) = 88*(n-1);  n-1 =  = 14;  hence,  n= 15.\r\n" );
document.write( "\r\n" );
document.write( "CHECK.  -396 + (15-1)*88 = use your calculator = 836,  correct.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To find the sum of this AP, use the general formula for the sum of an AP\r\n" );
document.write( "\r\n" );
document.write( "     = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It gives at n= 15\r\n" );
document.write( "\r\n" );
document.write( "     =  = use your calculator = 3300.   ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic progressions see \r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Now you see from my post (I hope), how much is it better
\n" ); document.write( "to post problems separately than to pack them in sets.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is the ONLY way to communicate with tutors in a respectful tone.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Do not forget to post your \" THANKS \" to me for my teaching.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );