How do I find the General Term of a Sequence?

In summary, the conversation discusses the difficulty in finding the general term of a complicated sequence and the need for an equation to determine it. It is mentioned that there is no general formula, but a pattern can be observed in the alternating positive and negative terms of the sequence. One suggestion for the general term is (-1)^n, but there is still uncertainty about the complete solution.
  • #1
XEROX_FAN
2
0
1. Write down the general term of each of the following sequences in simplest form:
So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ...

I really need to find an equation that I can use to determine the general term for any given sequence.

Homework Equations

?[/B] Umm trying to find one ...

The Attempt at a Solution

:[/B] tn = -n
and that's about as far as I got ...
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
XEROX_FAN said:
1. Write down the general term of each of the following sequences in simplest form:
So far I have been using guess and check to find the solutions, but it doesn't seem much use when you get to a sequence more complicated like this: 1, -4, 7, -10, 13, ...

I really need to find an equation that I can use to determine the general term for any given sequence.2. Homework Equations ? Umm trying to find one ...
3. The Attempt at a Solution : tn = -n
and that's about as far as I got ...

There really is no general formula to find the general term of a sequence. You essentially have to look for a pattern in the numbers.

Notice the terms in your sequence are alternating positive and negative. This tells you ##(-1)^n## will be part of the general term. What else do you notice?
 

Related to How do I find the General Term of a Sequence?

1. What is the general term of a sequence?

The general term of a sequence is an algebraic expression or formula that represents the pattern or rule governing the sequence. It is also known as the nth term or the recurrence relation.

2. How do I find the general term of a sequence?

To find the general term of a sequence, you need to identify the pattern or rule that relates the terms in the sequence. This can be done by looking at the differences between consecutive terms, multiplying or dividing by a constant, or using other mathematical operations. Once you have identified the pattern, you can write it as an algebraic expression to represent the general term.

3. Can a sequence have more than one general term?

No, a sequence can only have one general term. This term represents the overall pattern or rule of the sequence and should be able to generate any term in the sequence. However, there can be different ways to write the general term, depending on how you identify the pattern.

4. Is it possible to find the general term of any sequence?

Yes, it is possible to find the general term of any sequence as long as there is a clear pattern or rule governing the sequence. However, some sequences may have more complex or non-linear patterns, which can make it more challenging to find the general term.

5. How can finding the general term of a sequence be useful?

Finding the general term of a sequence can be useful in many ways. It allows you to predict or generate any term in the sequence without having to list out all the previous terms. It also helps to understand the underlying pattern or rule of the sequence, which can be applied to solve other mathematical problems. Additionally, finding the general term can be used to prove mathematical concepts and theories.

Similar threads

How to show that these sequences are summable?
    • Calculus and Beyond Homework Help
Replies
1
Views
503
Proving convergence of rational sequence
    • Calculus and Beyond Homework Help
Replies
2
Views
441
Converging Vs diverging sequences
    • Calculus and Beyond Homework Help
Replies
4
Views
1K
Prove that this series converges uniformly on R
    • Calculus and Beyond Homework Help
Replies
4
Views
581
Find the standard deviation of the values of ##y##
    • Calculus and Beyond Homework Help
Replies
3
Views
735
Why is this not a general solution to this nonlinear DE?
    • Calculus and Beyond Homework Help
Replies
5
Views
440
MHB Number patterns and sequences - Tn Term
    • General Math
Replies
1
Views
1K
I Finding a general formula for a recursive sequence
    • General Math
Replies
1
Views
1K
Why only odd cosine terms in this Fourier series?
    • Calculus and Beyond Homework Help
Replies
1
Views
460
How to Approach Solving a Nonlinear Second Order ODE with a Quadratic Term?
    • Calculus and Beyond Homework Help
Replies
4
Views
700

Hot Threads

Recent Insights

Back
Top