document.write( "Question 254764: determine the arithmetic sequence with first term 1 and common difference not equal to zero, whose second, tenth, and thirty fourth terms are the first 3 terms in geometric sequence. \n" ); document.write( "
Algebra.Com's Answer #187114 by palanisamy(496)\"\" \"About 
You can put this solution on YOUR website!
Let the arithmetic sequence be 1,1+d,1+2d,..... where d is the common difference.
\n" ); document.write( "Second term = 1+d
\n" ); document.write( "Tenth term = 1+(10-1)d = 1+9d
\n" ); document.write( "Thirty fourth term = 1+(34-1)d = 1+33d
\n" ); document.write( "Given, these three terms, 1+d,1+9d,1+33d are the first 3 terms in geometric sequence.
\n" ); document.write( "So we get, (1+9d)^2 = (1+d)(1+33d)
\n" ); document.write( " 1+81d^2+18d = 1+33d+d+33d^2
\n" ); document.write( " 81d^2+18d+1-33d^2-33d-d-1 = 0
\n" ); document.write( " 48d^2-16d = 0
\n" ); document.write( " 16d(3d-1) = 0
\n" ); document.write( " d = 0 or d = 1/3
\n" ); document.write( "Since d is nonzero, we get d = 1/3
\n" ); document.write( "Therefore the arithmetic sequence is 1,1+1/3,1+2/3,..
\n" ); document.write( " 1,4/3,5/3,...
\n" ); document.write( " \n" ); document.write( "
\n" );