document.write( "Question 1012250: Please help me solve this :\r
\n" ); document.write( "\n" ); document.write( "In an arithmetic progression a3=5 and a5=11 \r
\n" ); document.write( "\n" ); document.write( "Calculate the sum of 100 terms . \n" ); document.write( "

Algebra.Com's Answer #628115 by rothauserc(4718) $\"\"$ $\"About$

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for an arithmetic progression, the nth term is given by
\n" ); document.write( "An = A1 + d(n-1) where d is the common difference
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\n" ); document.write( "we have two equations in two unknowns
\n" ); document.write( "1) A3 = 5 = A1 + d(3-1)
\n" ); document.write( "A1 + 2d = 5
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\n" ); document.write( "2) A5 = 11 = A1 + d(5-1)
\n" ); document.write( "A1 + 4d = 11
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\n" ); document.write( "now subtract equation 1 from equation 2 and we get
\n" ); document.write( "2d = 6
\n" ); document.write( "d = 3
\n" ); document.write( "use equation 1 to find A1
\n" ); document.write( "A1 + 3(2) = 5
\n" ); document.write( "A1 = -1
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\n" ); document.write( "equation for the nth term is
\n" ); document.write( "An = -1 + 3(n-1)
\n" ); document.write( "We can check this by using equation 2
\n" ); document.write( "-1 + 3(5-1) = 11
\n" ); document.write( "-1 + 12 = 11
\n" ); document.write( "11 = 11
\n" ); document.write( "our equation checks out
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\n" ); document.write( "sum of the first n terms(Sn) = (n(A1 + An)) / 2
\n" ); document.write( "A1 = -1
\n" ); document.write( "A100 = -1 + 100(100-1) = 9899
\n" ); document.write( "S100 = (100(-1 + 9899)) / 2 = 494900\r
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