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The sum of three consecutive terms of an arithmetic sequence is 3. The sum of their squares is 75. find the three numbers
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\n" ); document.write( "Let a = the 2nd number in the sequence
\n" ); document.write( "Since an arithmetic sequence has a common difference, d, the 2nd number will a + d
\n" ); document.write( "And the 3rd number will be (a+d) + d = a + 2d
\n" ); document.write( "The sum of the three numbers is 3:
\n" ); document.write( "a + (a+d) + (a+2d) = 3
\n" ); document.write( "3a + 3d = 3
\n" ); document.write( "a + d = 1
\n" ); document.write( "a = 1 - d
\n" ); document.write( "The sum of squares is 75:
\n" ); document.write( "a^2 + (a+d)^2 + (a+2d)^2 = 75
\n" ); document.write( "Substitute a = 1-d:
\n" ); document.write( "(1-d)^2 + ((1-d)+d)^2 + ((1-d)+2d)^2 = 75
\n" ); document.write( "Solve for d:
\n" ); document.write( "1 + 2d + d^2 + 1 + 1 - 2d + d^2 = 75
\n" ); document.write( "3 + 2d^2 = 75
\n" ); document.write( "d^2 = 36
\n" ); document.write( "This gives d = 6, d = -6
\n" ); document.write( "Let's take d=6 [taking d=-6 gives the same 3 numbers-- check this]
\n" ); document.write( "So the 1st number a = 1 - d = -5
\n" ); document.write( "The 2nd number is -5 + 6 = 1
\n" ); document.write( "And the 3rd number is -5 + 2*6 = 7
\n" ); document.write( "Ans: -5,1,7
\n" ); document.write( "Check:
\n" ); document.write( "-5+1+7 = 3
\n" ); document.write( "25+1+49 = 75 \n" ); document.write( "