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Number patterns and sequences - Tn Term


New member
Feb 26, 2020
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


Well-known member
MHB Math Helper
Jan 29, 2012
If it is non- linear then it cannot be written in that form! Taking [tex]T_1= 3x+ 5y[/tex], [tex]T_2=5x[/tex], [tex]T_3= 7x-5y[/tex], and [tex]T_4= 9x-10y[/tex], then you want [tex]T_2= 5x= 3x+ 5y+ d[/tex] so [tex]d= 2x- 5y[tex]. But then you want
[tex]T_3= 7x- 5y= 3x+ 5y+ 2d[/tex] so [tex]d= (4x- 10y)/2= x- 10y[/tex]. Those are not the same so this sequence cannot be written in that way.
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