document.write( "Question 1088941: Thank you ikleyn for solving my question about the theater problem.\r
\n" ); document.write( "\n" ); document.write( "The sum of the the first nine terms of an arithmetic sequence is 99, and its seventh term is 19. What is its ninth term?\r
\n" ); document.write( "\n" ); document.write( "So far my solution is(Im unsure of my solution)
\n" ); document.write( "a7=19(Seventh term);a9=99(First nine terms); a9=?(Ninth term)\r
\n" ); document.write( "\n" ); document.write( "Sn=n/2(a1+an)
\n" ); document.write( "Sn=9/2(a1+a9)
\n" ); document.write( "99=4.5(a1 + ______) [Not sure what to add here]\r
\n" ); document.write( "\n" ); document.write( "a9=a6+a7+6d
\n" ); document.write( "a9=a7+19+6d
\n" ); document.write( "a9=a1+7d+19+6d
\n" ); document.write( "a9=a1+19+13d
\n" ); document.write( "2a1+19+13d\r
\n" ); document.write( "\n" ); document.write( "Basically I am not sure of my formula. If you don't seem to understand the problem, I have a sample problem(with solution) identical to this problem you can request it if you want. \n" ); document.write( "
Algebra.Com's Answer #703324 by MathTherapy(10556)\"\" \"About 
You can put this solution on YOUR website!
Thank you ikleyn for solving my question about the theater problem.\r
\n" ); document.write( "\n" ); document.write( "The sum of the the first nine terms of an arithmetic sequence is 99, and its seventh term is 19. What is its ninth term?\r
\n" ); document.write( "\n" ); document.write( "So far my solution is(Im unsure of my solution)
\n" ); document.write( "a7=19(Seventh term);a9=99(First nine terms); a9=?(Ninth term)\r
\n" ); document.write( "\n" ); document.write( "Sn=n/2(a1+an)
\n" ); document.write( "Sn=9/2(a1+a9)
\n" ); document.write( "99=4.5(a1 + ______) [Not sure what to add here]\r
\n" ); document.write( "\n" ); document.write( "a9=a6+a7+6d
\n" ); document.write( "a9=a7+19+6d
\n" ); document.write( "a9=a1+7d+19+6d
\n" ); document.write( "a9=a1+19+13d
\n" ); document.write( "2a1+19+13d\r
\n" ); document.write( "\n" ); document.write( "Basically I am not sure of my formula. If you don't seem to understand the problem, I have a sample problem(with solution) identical to this problem you can request it if you want.
\n" ); document.write( "
You were given the sum of the 1st 9 terms of the AP, and the 7th term so that the 1st term and d: the common difference, can be determined. \r\n" );
document.write( "Therefore, I would NOT USE the SUM of an AP formula you used but this instead: \"matrix%281%2C3%2C+S%5Bn%5D%2C+%22=%22%2C+%28n%2F2%29%282a%5B1%5D+%2B+%28n+-+1%29d%29%29\"\r\n" );
document.write( "\"S%5B9%5D+=+%289%2F2%29%282a%5B1%5D+%2B+%289+-+1%29d%29\" ---- Substituting 9 for n\r\n" );
document.write( "\"99+=+%289%2F2%29%282a%5B1%5D+%2B+8d%29\" --------- Substituting \"matrix%281%2C3%2C+99%2C+for%2C+S%5B9%5D%29\"\r\n" );
document.write( "\"198+=+9%282a%5B1%5D+%2B+8d%29\" ---------- Cross-multiplying\r\n" );
document.write( "\"198%2F9+=+2a%5B1%5D+%2B+8d\"\r\n" );
document.write( "\"22+=+2a%5B1%5D+%2B+8d\" ======> \"11+=+a%5B1%5D+%2B+4d\" -------- eq (i)\r\n" );
document.write( "\r\n" );
document.write( "\"a%5Bn%5D+=+a%5B1%5D+%2B+%28n+-+1%29d\"\r\n" );
document.write( "\"a%5B7%5D+=+a%5B1%5D+%2B+%287+-+1%29d\" -------- Substituting 7 for n\r\n" );
document.write( "\"19+=+a%5B1%5D+%2B+6d\" ------------- Substituting \"matrix%281%2C3%2C+19%2C+for%2C+a%5B7%5D%29\" ------- eq (ii)\r\n" );
document.write( "8 = 2d ------ Subtracting eq (i) from eq (ii)\r\n" );
document.write( "\"matrix%281%2C7%2C+8%2F2%2C+%22=%22%2C+d%2C+%22======%3E%22%2C+4%2C+%22=%22%2C+d%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"11+=+a%5B1%5D+%2B+4%284%29\" --------- Substituting 4 for d in eq (i)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\"a%5B9%5D+=+a%5B1%5D+%2B+8d+\"\r\n" );
document.write( "\"a%5B9%5D+=+-+5+%2B+8%284%29\" ------- Substituting – 5 for a1, and 4 for d\r\n" );
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