document.write( "Question 1043724: The fifth term of an arithmetic sequence is 9 and the 32nd term is -84. What is the 23rd term? \n" ); document.write( "
Algebra.Com's Answer #658877 by rothauserc(4718)\"\" \"About 
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The nth term of an arithmetic sequence is defined as
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\n" ); document.write( "an = a1 + d(n-1), where a1 is the first term and d is the common difference
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\n" ); document.write( "we are given two equations in two unknowns
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\n" ); document.write( "1) 9 = a1 +d(5-1)
\n" ); document.write( "2) -84 = a1 +d(32-1)
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\n" ); document.write( "solve equation 1) for a1
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\n" ); document.write( "a1 = 9 -4d
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\n" ); document.write( "substitute for a1 in equation 2)
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\n" ); document.write( "-84 = (9-4d) + 31d
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\n" ); document.write( "27d = -93
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\n" ); document.write( "d = -93/27 = -31/9
\n" ); document.write( "a1 = 9 -4(-31/9) = 81/9 +124/9 = 205/9
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\n" ); document.write( "check equation 1) and equation 2)
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\n" ); document.write( "9 = 205/9 + (-31/9)4 = 205/9 - 124/9 = 81/9 = 9
\n" ); document.write( "-84 = 205/9 + (-31/9)31 = 205/9 - 961/9 = -756/9 = -84
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\n" ); document.write( "our answers for a1 and d are correct
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\n" ); document.write( "we can calculate the 23rd term
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\n" ); document.write( "a23 = 205/9 + (-31/9)(22) = 205/9 -682/9 = -477/9 = -53
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\n" ); document.write( "The 23rd term is -53
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