Calculating nth Term of Sequences: What Now?

In summary, the conversation is about finding the value of n for which the nth term of a sequence is equal to 4 times the nth term of another sequence. The first sequence has a nth term of -2n+4 and the second sequence has a nth term of 2n-24. The question is asking for the value of n that satisfies the equation a_n = 4b_n.
  • #1
BerriesAndCream
4
2
Homework Statement
The nth term of the sequence 2, 0, -2, -4, -6 ... is 4 times the nth term of the sequence -22, -20, -18, -16, -14, ... Work out the value of n.
Relevant Equations
.
I don't understand what the question is asking.

the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.
 
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  • #2
BerriesAndCream said:
Homework Statement:: The nth term of the sequence 2, 0, -2, -4, -6 ... is 4 times the nth term of the sequence -22, -20, -18, -16, -14, ... Work out the value of n.
Relevant Equations:: .

I don't understand what the question is asking.

the nth term of the first sequence i can calculate to be -2n+4, while 2n-24 is the nth term for the second sequence. now what? The question isn't clear.
If ##a_n = -2n + 4## is the n-th term of the first sequence, and ##b_n = 2n - 24## is the n-th term of the second sequence, what they're asking is this: For which value of n is ##a_n = 4b_n##?
 
  • #3
Mark44 said:
If ##a_n = -2n + 4## is the n-th term of the first sequence, and ##b_n = 2n - 24## is the n-th term of the second sequence, what they're asking is this: For which value of n is ##a_n = 4b_n##?
oh... all clear now. thank you.
 
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Likes WWGD and berkeman

1. What is the nth term of a sequence?

The nth term of a sequence is the general formula or pattern that can be used to find any term in the sequence. It is usually denoted as an, where n represents the position of the term in the sequence.

2. How do you calculate the nth term of a sequence?

To calculate the nth term of a sequence, you need to first identify the pattern or rule that the sequence follows. This can be done by looking at the differences between consecutive terms or by finding a common ratio between terms. Once the pattern is identified, you can use it to create a general formula for the nth term.

3. What is the difference between an arithmetic and geometric sequence?

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

4. Can the nth term of a sequence be negative?

Yes, the nth term of a sequence can be negative. This depends on the pattern or rule that the sequence follows. Some sequences may have negative terms, while others may not.

5. How can the nth term of a sequence be used?

The nth term of a sequence can be used to find any term in the sequence without having to list out all the previous terms. It can also be used to predict future terms in the sequence and to identify any patterns or relationships between terms. Additionally, the nth term can be used in real-life situations, such as predicting population growth or financial investments.

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