document.write( "Question 1189816: Find the number of terms in sequence 12;7;2;....;-203
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #821298 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "As you see, and it is almost obvious, this sequence is an arithmetic progression.\r\n" );
document.write( "\r\n" );
document.write( "The first term is 12 and the common difference is -5.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "On the number line, the distance between the first term and the last term is \r\n" );
document.write( "\r\n" );
document.write( "    12 + 203 = 215.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The number of gaps between the terms in the number line is   = 43.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Add 1 (one) to it, and you will get the number of terms of the progression: it is 43 + 1 = 44.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is the simplest way to solve this and hundreds other similar problems.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Your intuition and your common sense will dictate you what to do . . . without memorizing any formulas.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "CHECK.   To check, calculate the last term, using standard formula of an arithmetic progression\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "          =  = 12 - 43*5 = - 203.    ! Correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );