Answer:
Explanation:
To find the explicit formula for the sequence 31, 27, 23, ..., we first need to find the common difference between consecutive terms.
We can see that each term is obtained by subtracting 4 from the previous term. Therefore, the common difference is -4.
Using the general formula for an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the index of the term we want to find.
In this sequence, a1 = 31 and d = -4. So, we have:
an = 31 + (n - 1)(-4)
Simplifying, we get:
an = 35 - 4n
Therefore, the explicit formula for the n-th term of the sequence 31, 27, 23, ... is an = 35 - 4n.