document.write( "Question 1015443: Please help with this question.how many terms in the series 19+16+13+...must be added to give a sum of 44? \n" ); document.write( "

Algebra.Com's Answer #631802 by rothauserc(4718) $\"\"$ $\"About$

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the sum of n terms of an arithmetic sequence is,
\n" ); document.write( "Sn = (n/2) * (2a1 + (n-1)d) where a1 is the first term to sum, d is the common difference between terms, n is the number of terms to sum
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\n" ); document.write( "For our problem, Sn=44, d=-3, a1=19
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\n" ); document.write( "44 = (n/2) * (2(19) + (-3)(n-1))
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\n" ); document.write( "88 = n * ( 38 - 3n + 3)
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\n" ); document.write( "88 = n * (41 - 3n)
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\n" ); document.write( "88 = 41n - 3n^2
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\n" ); document.write( "3n^2 - 41n +88 = 0
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\n" ); document.write( "factor the polynomial
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\n" ); document.write( "(3n-8) * (n-11) = 0
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\n" ); document.write( "there are two possibilities
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\n" ); document.write( "n = 11 or n = 8/3
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\n" ); document.write( "now, we want the nth term, so we can reject n = 8/3
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\n" ); document.write( "Therefore, 11 terms in the sequence must be summed to get 44 \n" ); document.write( "

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