Number patterns and sequences - Tn Term

In summary, the given number sequence cannot be written in the form of a general term as it is non-linear. The suggested formula, Tn=T1+d(n-1), does not hold true for all values in the sequence.
  • #1
JanleyKrueger
1
0
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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  • #2
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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FAQ: Number patterns and sequences - Tn Term

What is a "Tn term" in a number pattern or sequence?

A Tn term refers to the nth term in a sequence, where n is the position of the term in the sequence. For example, in the sequence 2, 4, 6, 8, 10, the T3 term would be 6, as it is the third term in the sequence.

How do you find the Tn term in a number pattern or sequence?

To find the Tn term in a number pattern or sequence, you can use the formula Tn = a + (n-1)d, where a is the first term in the sequence and d is the common difference between each term. Simply substitute the values for a and d and solve for Tn.

What is the difference between an arithmetic and geometric sequence?

An arithmetic sequence is a sequence in which each term is found by adding a constant value to the previous term, while a geometric sequence is a sequence in which each term is found by multiplying the previous term by a constant value. In an arithmetic sequence, the common difference between each term is constant, while in a geometric sequence, the common ratio between each term is constant.

How can you determine the next term in a number pattern or sequence?

To determine the next term in a number pattern or sequence, you can use the formula Tn+1 = Tn + d, where Tn is the current term and d is the common difference or ratio. Alternatively, you can look for a pattern in the sequence and use deductive reasoning to determine the next term.

How are number patterns and sequences used in real life?

Number patterns and sequences are used in various fields such as mathematics, science, and technology. In mathematics, they are used to solve problems and make predictions. In science, they are used to model natural phenomena and make predictions about future events. In technology, they are used in coding and data analysis. Number patterns and sequences are also used in everyday life, such as in music, art, and sports.

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