Final answer:
The first three terms of the arithmetic sequence with a third term of 15 and a sum of the first 10 terms equal to 125 are 5, 10, and 15.
Step-by-step explanation:
The question asks for the first three terms of an arithmetic sequence where the third term is 15 and the sum of the first 10 terms is 125. To find the first term (a) and the common difference (d) of the sequence, we use two equations derived from the given information. The third term can be expressed as a + 2d = 15, and the sum of the first 10 terms is given by 10/2(2a + (10 - 1)d) = 125.
By solving these two equations simultaneously, we can find a and d. From the first equation, we express d in terms of a: d = (15 - a)/2. Substituting this into the sum formula and solving for a, we get a + 45 - 5a = 125, hence a = 5. Plugging a back into the expression for d, we obtain d = 5. Therefore, the first three terms of the sequence are 5, 10, and 15.