document.write( "Question 842180: 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 #507461 by josgarithmetic(39618) $\"\"$ $\"About$

You can put this solution on YOUR website!
The first term of the SEQUENCE is 19.
\n" ); document.write( "The difference between terms is NEGATIVE 3.
\n" ); document.write( "The n term of the SEQUENCE is $\"19%2B%28n-1%29%2A%28-3%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The formula for Arithmetic SERIES is $\"%28n%2F2%29%28a%5B1%5D%2Ba%5Bn%5D%29\"$ .\r
\n" ); document.write( "\n" ); document.write( "You want this equation: $\"highlight_green%28%28n%2F2%29%2819%2B19%2B%28n-1%29%2A%28-3%29%29=44%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "SOLUTION STEPS
\n" ); document.write( " $\"%28n%2F2%29%2838%2B%28-3n%2B3%29%29=44\"$
\n" ); document.write( " $\"n%2841-3n%29=88\"$
\n" ); document.write( " $\"41n-3n%5E2=88\"$
\n" ); document.write( " $\"3n%5E2-41n%2B88=0\"$
\n" ); document.write( " $\"Discriminant+=+625\"$ and $\"sqrt%28625%29=25\"$ ; this is done for using general solution to a quadratic equation and avoid trying to factor the quadratic expression.
\n" ); document.write( "-
\n" ); document.write( " $\"n=%2841%2B-+25%29%2F%286%29\"$ without showing all the steps for this formula.
\n" ); document.write( "The MINUS form will give a bad value, a mixed number while the PLUS form gives $\"highlight%28highlight%28n=11%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "What you might try, to be sure, find the sum of this:
\n" ); document.write( " $\"19%2B16%2B13%2B10%2B7%2B4%2B1%2B%28-2%29%2B%28-5%29%2B%28-8%29%2B%28-11%29\"$ \n" ); document.write( "

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