document.write( "Question 1106455: Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92. \n" ); document.write( "

Algebra.Com's Answer #721437 by rothauserc(4718) $\"\"$ $\"About$

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The middle term of a 15 term sequence is 92 so this is the eighth term.
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\n" ); document.write( "The eighth term(92) of this arithmetic sequence is
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\n" ); document.write( "92 = a(1) + 7d
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\n" ); document.write( "Therefore, the last term is 7 terms further in the sequence, so it is 92 + 7d
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\n" ); document.write( "Likewise, the first term is 7 terms before the 8th term, so it is 92 - 7d.
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\n" ); document.write( "The sum of the first and last term is (92 - 7d) + (92 + 7d) = 92 + 92 = 184
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\n" ); document.write( "The sum of this arithmetic sequence is
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\n" ); document.write( "(1/2) * 15 * 184 = 1380
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\n" ); document.write( "Note the sum of an arithmetic sequence is (1/2) * n * (x(1) + x(n)), where n is the number of terms, x(1) is the first term and x(n) is the nth term
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