MHB Number patterns and sequences - Tn Term

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The sequence presented is 3x+5y, 5x, 7x-5y, 9x-10y, and the user is attempting to find a general term Tn in the form Tn=T1+d(n-1). It is concluded that the sequence is non-linear, which means it cannot be expressed in that linear format. Calculating the differences, d, between terms yields inconsistent results, indicating that the sequence does not follow a linear pattern. The analysis shows that the differences derived from the terms do not match, confirming the non-linearity of the sequence. Therefore, a general term in the proposed linear format is not feasible.
JanleyKrueger
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The number sequence is as follows:

3x+5y; 5x; 7x-5y; 9x-10y...

I need to formulate a general term - Tn=T1+d(n-1)
In the above sequence I have no idea what.
I also think this sequence is non linear.
Please help with a solution
Thanks
 
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If it is non- linear then it cannot be written in that form! Taking T_1= 3x+ 5y, T_2=5x, T_3= 7x-5y, and T_4= 9x-10y, then you want T_2= 5x= 3x+ 5y+ d so d= 2x- 5y. But then you want <br /> T_3= 7x- 5y= 3x+ 5y+ 2d so d= (4x- 10y)/2= x- 10y. Those are not the same so this sequence cannot be written in that way.
 
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Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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