document.write( "Question 879030: I am trying to find the sum of the following sequence:32+33+34+35+...+113. I can do any when it starts with 1, but I cannot grasp how to solve this one.\r
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Algebra.Com's Answer #530457 by josgarithmetic(39625) $\"\"$ $\"About$

You can put this solution on YOUR website!
You can derive a specific expression for the sum, without using the formula, if you want.\r
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\n" ); document.write( "\n" ); document.write( "How many terms are in your sum? You see the difference between terms is 1; if you only had 32+33+34, this is three terms to sum. 34-32=2, but add 1 more to get 3; meaning three terms. YOUR given summation uses (113-32)+1=82 terms.\r
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\n" ); document.write( "\n" ); document.write( "Now if you had, 32+33+34, and you add to it 34+33+32, you can show:
\n" ); document.write( " $\"%2832%2B33%2B34%29%2B%2834%2B33%2B32%29\"$
\n" ); document.write( " $\"32%2B33%2B34%2B34%2B33%2B32\"$
\n" ); document.write( " $\"32%2B34%2B33%2B33%2B34%2B32\"$
\n" ); document.write( " $\"%2832%2B34%29%2B%2833%2B33%29%2B%2834%2B32%29\"$ , commutative property for addition
\n" ); document.write( " $\"66%2B66%2B66\"$
\n" ); document.write( " $\"3%2866%29\"$
\n" ); document.write( "In partial wording, $\"n%28firstTerm%2BlastTerm%29\"$ , and n is for how many terms in the sum. YOUR sum has first term 32 and last term 113, and since the little example I showed was for DOUBLE the sum, you want to divide by 2:
\n" ); document.write( " $\"highlight%28%28n%2F2%29%28firstTerm%2BlastTerm%29%29\"$
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\n" ); document.write( "Your example has n=82, firstTerm=32, lastTerm=113.
\n" ); document.write( "The sum wanted is $\"highlight%28%2882%2F2%29%2832%2B113%29%29\"$ . Just compute the number. \n" ); document.write( "

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