document.write( "Question 250532: Find n for a series for which a1=9, d=4.5, and Sn=40.5 \n" ); document.write( "
Algebra.Com's Answer #185063 by drk(1908)\"\" \"About 
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We have the nth term formula as
\n" ); document.write( "T(n) = a1 + d(n-1)
\n" ); document.write( "From this we have
\n" ); document.write( "T(n) = 9 + 4.5(n-1)
\n" ); document.write( "or
\n" ); document.write( "T(n) = 4.5n + 4.5
\n" ); document.write( "The sum of this is
\n" ); document.write( "SUM(n=1 to k) [4.5n + 4.5] is
\n" ); document.write( "4.5(k(k+1))/2 + 4.5k = 40.5
\n" ); document.write( "multiplying both sides by 2, we get
\n" ); document.write( "4.5k^2 + 4.5k + 9k = 81
\n" ); document.write( "4.5k^2 + 13.5k - 81 = 0.
\n" ); document.write( "By quadratic, we get
\n" ); document.write( "k = 3 or k = -6.
\n" ); document.write( "After 3 terms we get the sum of 40.5.\r
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