Number patterns and sequences - Tn Term

Click For Summary
SUMMARY

The discussion centers on the formulation of a general term for the non-linear sequence defined by the terms 3x+5y, 5x, 7x-5y, and 9x-10y. The initial term is T1=3x+5y, and subsequent terms are derived as T2=5x, T3=7x-5y, and T4=9x-10y. The analysis reveals that the common difference 'd' cannot be consistently defined across the sequence, confirming its non-linear nature and indicating that it cannot be expressed in the form Tn=T1+d(n-1).

PREREQUISITES
  • Understanding of algebraic sequences and series
  • Familiarity with non-linear equations
  • Basic knowledge of mathematical notation and terminology
  • Experience with variable manipulation in algebra
NEXT STEPS
  • Study non-linear sequences in algebra
  • Explore the concept of common differences in sequences
  • Learn about polynomial sequences and their characteristics
  • Investigate mathematical proofs related to sequence behavior
USEFUL FOR

Mathematics students, educators, and anyone interested in advanced algebraic concepts, particularly those focusing on sequences and series.

JanleyKrueger
Messages
1
Reaction score
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
 
Mathematics news on Phys.org
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.
 
Last edited by a moderator:

Similar threads

MHB (Seemingly) Random Sequences
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Is There a Hidden Pattern in This Sequence of Numbers?
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Is this Recursive Pattern in the Collatz Sequence Known?
  • · Replies 3 ·
Replies
3
Views
886
MHB Arithmetic Sequence Confusion // a{n-1} and a{n+1}
  • · Replies 1 ·
Replies
1
Views
2K
High School What is the formula for this sequence for n-th number
  • · Replies 5 ·
Replies
5
Views
2K
MHB How to Solve a Geometric Sequence with Given Differences?
  • · Replies 2 ·
Replies
2
Views
3K
MHB Help Me Find the Perimeter of Tn+1
  • · Replies 4 ·
Replies
4
Views
3K
MHB Find the 79th term in the sequence
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad 1)A sequence is defined by Tn= Tn-2/Tn-1 for n>=3 with T1=20 and T2=2.
  • · Replies 1 ·
Replies
1
Views
4K
MHB Geometric Sequences help - (3 given terms, find the rest)
  • · Replies 18 ·
Replies
18
Views
7K