Final answer:
The explicit formula for the nth term of the sequence is an = 1 × (2/3)n-1, which follows the structure of a geometric sequence with a common ratio of 2/3.
Step-by-step explanation:
Finding an Explicit Formula for the nth Term
To find an explicit formula for the nth term of the sequence 1, 2/3, 1/3, 4/27, we notice a pattern in both the numerators and denominators that is suggestive of a geometric sequence. In a geometric sequence, each term is produced by multiplying the previous term by a fixed ratio. In this case, the ratio appears to be the fraction 2/3.
The first term of the sequence, known as a1, is 1. The nth term of a geometric sequence can be found using the formula:
an = a1 × rn-1
where r is the common ratio. Substituting the given values into this formula, the nth term an of the sequence is:
an = 1 × (2/3)n-1
This formula represents the explicit series expansion for the given sequence.