Answer :

Final answer:

To find x and y given an arithmetic sequence, we first solve for the common difference. Using the solved common difference 'd', we can then solve for x and y. Here, the solutions are x = 1058.333 and y = 2091.666.

Explanation:

In an arithmetic sequence, the difference between any two successive terms is constant. This difference is referred to as the common difference. For this given sequence: 25, x, y, 3125, we can denote the common difference by 'd'.

Because x is the term following 25, we can write x = 25 + d.

Similarly, as y is the term following x, we can write y = x + d = (25 + d) + d = 25 + 2d.

The term following y is given as 3125, which means that 3125 = y + d = (25 + 2d) + d = 25 + 3d.

Therefore, not knowing d, x, and y, yet, we can solve for d by using the given equation: 3125 = 25 + 3d, which simplifies to 3100 = 3d, hence d = 3100 / 3 = 1033.333.

Now, having the value of d, we can substitute it into the formulas mentioned earlier to obtain: x = 25 + d = 25 + 1033.333 = 1058.333 and y = 25 + 2d = 25 + 2 * 1033.333 = 2091.666.

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