document.write( "Question 1035723: the 1st term of A.P is -12 and last term is 40. if the sum of the series is 196,find the number of terms and the common difference. \n" ); document.write( "

Algebra.Com's Answer #650376 by rothauserc(4718) $\"\"$ $\"About$

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x1 = -12
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\n" ); document.write( "1) 40 = -12 + d(n-1), where n is the nth term and d is the common difference
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\n" ); document.write( "2) 196 = (n/2) * ( 2*(-12) + (n-1)*d)
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\n" ); document.write( "solve equation 1 for d and substitute in equation 2
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\n" ); document.write( "d = 52 / (n-1)
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\n" ); document.write( "196 = (n/2) * (2*(-12) + (n-1)*52/(n-1))
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\n" ); document.write( "196 = (n/2) * (-24 + 52)
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\n" ); document.write( "196 = 14n
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\n" ); document.write( "n = 14
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\n" ); document.write( "substitute in equation 1 to find d
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\n" ); document.write( "40 = -12 + d * (14 -1)
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\n" ); document.write( "13d = 52
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\n" ); document.write( "d = 4
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\n" ); document.write( "the number of terms is 14
\n" ); document.write( "the common difference is 4
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