document.write( "Question 1149896: How many terms has an arithmetic \"highlight%28cross%28progreression%29%29\" progression where sum is 1340 with first term 3 and nth term 131? \n" ); document.write( "
Algebra.Com's Answer #771240 by ikleyn(52903)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "For any arithmetic progression of n terms  \"a%5B1%5D\", \"a%5B2%5D\", \"a%5B3%5D\" . . . \"a%5Bn%5D\",  the formula for its sum S works\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    S = \"%28%28a%5B1%5D+%2B+a%5Bn%5D%29%2F2%29%2An\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In our case, it gives\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    1340 = \"%28%283+%2B+131%29%2F2%29%2An\" = \"%28134%2F2%29%2An\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence,\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    n = \"%282%2A1340%29%2F134\" = 2*10 = 20.   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The number of the terms in the progression is 20.\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( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );