document.write( "Question 1137789: Find the sum of the arithmetic series with first term 1,common difference 3,and last term hundred \n" ); document.write( "

Algebra.Com's Answer #755678 by rothauserc(4718) $\"\"$ $\"About$

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The sum of the first n terms of an arithmetic sequence is
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\n" ); document.write( "Sum = (n/2) * (2a +d(n-1)), where a is the first term, n is the number of terms to sum, and d is the common difference
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\n" ); document.write( "We are given a=1, d=3
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\n" ); document.write( "We need to determine the nth term of this sequence which is 100
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\n" ); document.write( "The formula for the nth term of an arithmetic sequence is
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\n" ); document.write( "x(n) = x(1) +d(n-1), where x(1) is the first term
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\n" ); document.write( "we are given that the nth term is 100
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\n" ); document.write( "100 = 1 +3(n-1)
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\n" ); document.write( "100 = 1 +3n-3
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\n" ); document.write( "3n = 102
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\n" ); document.write( "n = 34
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\n" ); document.write( "sum = (34/2) * (2(1) +3(34-1))
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\n" ); document.write( "sum = 17 * (2 +99) = 1717
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