document.write( "Question 977391: the sum of the first n terms of the arithmetic progression 5,10,15... is 275 .how many terms are there in the sequence? \n" ); document.write( "

Algebra.Com's Answer #598897 by rothauserc(4718) $\"\"$ $\"About$

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Sn = (n * (a1 + an)) / 2
\n" ); document.write( "an = a1 + (n - 1) * d
\n" ); document.write( "an = 5 + (n - 1) * 5
\n" ); document.write( "an = 5n
\n" ); document.write( "therefore
\n" ); document.write( "275 = (n * (5 + 5n)) / 2
\n" ); document.write( "275 = (5n + 5n^2) / 2
\n" ); document.write( "550 = 5n + 5n^2
\n" ); document.write( "110 = n + n^2
\n" ); document.write( "n^2 +n -110 = 0
\n" ); document.write( "(n+11)*(n-10) = 0
\n" ); document.write( "n = -11 or n = 10
\n" ); document.write( "we want the positive n
\n" ); document.write( "There are 10 terms in the sequence
\n" ); document.write( "check our answer
\n" ); document.write( "an = 50 and
\n" ); document.write( "275 = (10 * 55) / 2
\n" ); document.write( "275 = 275
\n" ); document.write( "our answer checks
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