Final answer:
The explicit formula for the nth term of the sequence 25, 27, 29, an arithmetic sequence with a common difference of 2, is given by an = 23 + 2n. This formula allows us to find any term of the sequence by plugging in the value of n.
Step-by-step explanation:
To write an explicit formula for the nth term of the sequence 25, 27, 29, we can see that it is an arithmetic sequence where each term increases by 2. The first term, a1, is 25. You can find any term in an arithmetic sequence using the formula an = a1 + (n - 1)d, where d is the common difference between the terms. Here, d = 2. So for our sequence, the explicit formula would be an = 25 + (n - 1)×2. Simplifying this, we get an = 23 + 2n.
To validate this, let's check for n=1 (should be 25): a1 = 23 + 2(1) = 25, which matches the first term. And for n=2 (should be 27): a2 = 23 + 2(2) = 27, which is correct as well and so on.