document.write( "Question 484324: In the arithmetic sequence, the 3rd term is 4 and the 8th term is 49. Find the 1st term, the common difference and the sum of the first ten terms. \n" ); document.write( "
Algebra.Com's Answer #331393 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
In the arithmetic sequence, the 3rd term is 4 and the 8th term is 49. Find the 1st term, the common difference and the sum of the first ten terms.
\n" ); document.write( "
\r\n" );
document.write( "\"a%5Bn%5D=a%5B1%5D%2B%28n-1%29d\"\r\n" );
document.write( "\r\n" );
document.write( ">>...the 3rd term is 4...<<\r\n" );
document.write( "\r\n" );
document.write( "\"a%5B3%5D=a%5B1%5D%2B%283-1%29d\"\r\n" );
document.write( "\"4=a%5B1%5D%2B2d\"\r\n" );
document.write( "\"a%5B1%5D%2B2d=4\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( ">>...the 8th term is 49...<<\r\n" );
document.write( "\r\n" );
document.write( "\"a%5B8%5D=a%5B1%5D%2B%288-1%29d\"\r\n" );
document.write( "\"49=a%5B1%5D%2B7d\"\r\n" );
document.write( "\"a%5B1%5D%2B7d=49\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So we have a system of equations:\r\n" );
document.write( "\r\n" );
document.write( "\"system%28a%5B1%5D%2B2d=4%2Ca%5B1%5D%2B7d=49%29\"\r\n" );
document.write( "\r\n" );
document.write( "Solve by substitution or elimination and get\r\n" );
document.write( "\r\n" );
document.write( "\"a%5B1%5D=-14\" and \"d=9\"\r\n" );
document.write( "\r\n" );
document.write( "first term is -14,\r\n" );
document.write( "\r\n" );
document.write( "Here is the sequence to 10 terms:\r\n" );
document.write( "\r\n" );
document.write( "-14, -5, 4, 13, 22, 31, 40, 49, 58, 67 \r\n" );
document.write( "\r\n" );
document.write( "To get the sum of the first 10 terms, \r\n" );
document.write( "we use the formula:\r\n" );
document.write( "\r\n" );
document.write( "\"S%5Bn%5D+=+expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"S%5B10%5D+=+expr%2810%2F2%29%282%28-14%29%2B%2810-1%299%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"S%5B10%5D+=+5%28-28%2B%289%299%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"S%5B10%5D+=+5%28-28%2B81%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"S%5B10%5D+=+5%2853%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"S%5B10%5D+=+265\"\r\n" );
document.write( "\r\n" );
document.write( "sum =  265\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );