Explanation:
So, to find the formula for an arithmetic sequence, we need to figure out the first term and the common difference. The formula for these sequences involves adding a constant difference to each term to get the next one. In our case, we know that the third term is 12 and that each term is doubling by 2 each time. This tells us that the common difference is 2. Now we can work backwards from the third term and divide by 2 twice to find that the first term is 3. With those values, we can use the arithmetic sequence formula to find the explicit equation: aₙ = a₁ + (n - 1) * d. If we plug in our values, we end up with aₙ = 3 + (n - 1) * 2, which simplifies to aₙ = 2n + 1. This equation lets you find any term in the sequence by putting in the term number (n).