Discovering the Formula for a Repeating Sequence

In summary, a sequence formula is an equation that can be used to determine the value of any term in a sequence of numbers. To find the sequence formula, one must first identify the pattern in the sequence and use it to write the formula. There are different forms of sequence formulas such as explicit and recursive, with the main difference being how they calculate the value of a term. To check the correctness of a sequence formula, one can plug in different values and compare the results with the actual values in the sequence. However, it should be noted that sequence formulas can only be used for finite sequences with a clear pattern and cannot be applied to infinite or randomly patterned sequences.
  • #1
SciSteve
19
0
I have to find a formula for the general term of An for this sequence assuming that the pattern follows and continues. (13,3,13,3...)
I don't think there's any straightforward formulas to use for sequences and series' in finding a formula.
My attempt involved finding two numbers that add to 13 and subtract to 3 which is 8 and 5, but what I'm stuck on is inserting the n variable so that the pattern will keep repeating 13,3,13,3..so on. Totally lost on how to do it and it doesn't even seem that hard.
 
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  • #2
Try A_n = 8 + 5*(-1)^(n+1).
 
  • #3
figured it out thanks for the tip
 

What is a sequence formula?

A sequence formula is an equation that can be used to determine the value of any term in a sequence of numbers. It can be represented in various forms such as explicit, recursive, or general.

How do you find the sequence formula?

To find the sequence formula, you need to first identify the pattern in the sequence. This can be done by looking at the difference or ratio between consecutive terms. Once the pattern is identified, you can use it to write the sequence formula in the desired form.

What is the difference between an explicit and a recursive sequence formula?

An explicit sequence formula directly calculates the value of a term in the sequence based on its position, while a recursive sequence formula uses the previous terms in the sequence to calculate the value of the next term.

How can I check if my sequence formula is correct?

You can check if your sequence formula is correct by plugging in different values for the position of the term and comparing the result with the corresponding value in the sequence. Additionally, you can also use the formula to predict the value of the next few terms in the sequence and see if they match with the actual values.

Can the sequence formula be used to find any type of sequence?

No, the sequence formula can only be used to find the value of terms in a finite sequence. It cannot be used for infinite sequences or sequences with a random pattern.

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