The explicit formula for the nth term of the sequence is an=23+4(n−1).
In an arithmetic sequence, each term is obtained by adding a constant difference to the previous term. The explicit formula an=a1+(n−1)d provides a clear representation of this relationship. Here, an represents the nth term, a1 is the first term, n is the term number, and d is the common difference.
For the given sequence 23, 27, 31, ..., the common difference is 4, as each term increases by 4 compared to the previous one. The first term (a1) is 23. Substituting these values into the explicit formula, we get an=23+4(n−1). This formula enables us to find any term in the sequence by plugging in the corresponding term number. It's a concise way to express the relationship within an arithmetic sequence.