document.write( "Question 713096: Find the sum of all the even integers between 80 and 196 \n" ); document.write( "

Algebra.Com's Answer #438307 by htmentor(1343) $\"\"$ $\"About$

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Find the sum of all the even integers between 80 and 196
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\n" ); document.write( "This is an arithmetic sequence with a_1 = 80 and common difference, d = 2 [even integers]
\n" ); document.write( "The general formula for the n-th term of an arithmetic sequence is a_n = a_1 + (n-1)d
\n" ); document.write( "So in this case we have a_n = 80 + (n-1)2 -> a_n = 2n + 78
\n" ); document.write( "We need to find n for the last term, 196:
\n" ); document.write( "196 = 2n + 78 -> 2n = 118 -> n = 59
\n" ); document.write( "The formula for the sum of the first n terms of a arithmetic sequence is
\n" ); document.write( "S = (n/2)(a_1 + a_n)
\n" ); document.write( "S = (59/2)(80 + 196) = 8142 \n" ); document.write( "

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