- #1
intervoxel
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What is the recurrence formula for the sequence
[3,5,13,27,55,...]
Thank you for any help.
[3,5,13,27,55,...]
Thank you for any help.
You are right. It is 6 instead of 5. Thank you for the valuable link.mfb said:There is an infinite set of formulas that lead to this sequence.
Unless you made a typo, all of them are somewhat ugly.
The recurrence formula for this sequence is an = 2an-1 + an-2, where an represents the nth term in the sequence. This means that each term is equal to twice the previous term plus the term before that.
The recurrence formula is derived by observing the pattern in the sequence. Each term is the sum of the two previous terms multiplied by 2. This can be expressed in the form of an = 2an-1 + an-2, which is the general form for a recurrence formula.
Yes, the recurrence formula can be used to find any term in the sequence by plugging in the appropriate values for n. For example, to find the 7th term, we would substitute n = 7 into the formula and solve for a7.
No, there are other ways to generate this sequence. For example, we could use a closed-form formula, which is an explicit equation that gives the value of any term in the sequence without having to rely on previous terms. In this case, the closed-form formula for the sequence is an = 2n - 1.
Yes, the recurrence formula can be used for other sequences. It is a general form that can be applied to many different types of sequences, as long as there is a pattern that can be described by a formula. Recurrence formulas are commonly used in mathematics, computer science, and other scientific fields.