To accurately answer this question, we need to know the specific series being referenced. The question is currently incomplete. However, I can explain what an explicit rule is for common types of sequences. If you provide the sequence in question, I can give a specific answer.
Understanding Explicit Rules
An explicit rule (or formula) allows you to calculate any term in a sequence directly, without needing to know the previous terms. It defines the nth term (an) as a function of n, where n is the term number.
Explicit Rule for an Arithmetic Sequence
As mentioned in the reference, the explicit formula for an arithmetic sequence is:
an = a + (n - 1)d
Where:
- an is the nth term of the sequence.
- a is the first term of the sequence (a1).
- n is the term number (e.g., 1 for the first term, 2 for the second term, etc.).
- d is the common difference between consecutive terms.
Example:
Let's say we have an arithmetic sequence: 2, 5, 8, 11, ...
- a = 2 (the first term)
- d = 3 (the common difference)
Therefore, the explicit rule for this sequence would be:
an = 2 + (n - 1)3
an = 2 + 3n - 3
an = 3n - 1
We can use this to find, for example, the 10th term:
a10 = 3(10) - 1 = 29
Other Types of Sequences
While the arithmetic sequence is a common example, explicit rules can also be defined for geometric and harmonic sequences, as well as others. The form of the explicit rule will depend on the specific type of sequence.
In summary, to provide the exact explicit rule for your series, please provide the sequence itself. I can then apply the appropriate formula to determine the explicit rule.
