document.write( "Question 942261: In an arithmetic series, how can I find the value of the first term, given the 14th term equals 200 and the sum of the first 20 terms equals 3230. \n" ); document.write( "
Algebra.Com's Answer #574416 by stanbon(75887)\"\" \"About 
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In an arithmetic series, how can I find the value of the first term, given the 14th term equals 200 and the sum of the first 20 terms equals 3230.
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\n" ); document.write( "a(14) = a(1) + 13d = 200
\n" ); document.write( "3230 = (20/2)(a(1)+a(20))
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\n" ); document.write( "Rearrange::
\n" ); document.write( "a(1) + 13d = 200
\n" ); document.write( "a(1) + a(20) = 323
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\n" ); document.write( "a(20)- 13d = 123
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\n" ); document.write( "Note:: a(20) = a(14)+6d = 200 + 6d
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\n" ); document.write( "So, 200+6d - 13d = 123
\n" ); document.write( "-7d = -77
\n" ); document.write( "d = 11
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\n" ); document.write( "Solve for a(1)::
\n" ); document.write( "a(14) = a(1) + 13d = 200
\n" ); document.write( "a(1) = 200-13*11
\n" ); document.write( "a(1) = 200-143
\n" ); document.write( "a(1) = 57
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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