given a3 = -15, S10 = 125, find d and a10.

The problem is about arithmetic sequences. In an arithmetic sequence, the difference between any two successive terms is constant, and this difference is called the common difference, denoted by 'd'. The nth term of an arithmetic sequence can be found by the formula:

an = a1 + (n-1)*d

where an is the nth term, a1 is the first term, and n is the term number.

Also, the sum of the first n terms, Sn, of an arithmetic sequence can be found by the formula:

Sn = n/2 * (a1 + an)

where Sn is the sum of the first n terms, n is the term number, a1 is the first term, and an is the nth term.

From the problem, we know that a3 = -15 and S10 = 125. We need to find 'd' and a10.

Step 1: Express a3 in terms of a1 and d We know that a3 = a1 + 2d. Given that a3 = -15, we can write the equation as: a1 + 2d = -15 ----(equation 1)

Step 2: Express S10 in terms of a1, a10 and d We know that S10 = 10/2 * (a1 + a10) = 5 * (a1 + a10). Given that S10 = 125, we can write the equation as: 5 * (a1 + a10) = 125 a1 + a10 = 25 ----(equation 2)

Step 3: Solve the system of equations We can solve the system of equations (equation 1 and equation 2) to find the values of a1, a10 and d.

Please note that without additional information, we cannot solve this system of equations to find unique values for a1, a10 and d. We need at least one more equation or piece of information to solve this system.