Find the indicated terms of the geometric sequence with the given description.
The third term is 50 and the sixth term is $-\frac{3125}{256}$. Find the first and second terms. first term second term

Step 1 ：First, we need to find the common ratio. We know that the ratio between the sixth term and the third term is the cube of the common ratio, so we have \(r^3 = \frac{-3125}{256} \div 50 = \frac{-3125}{12800} = -\frac{625}{2560} = -\frac{125}{512}\). Therefore, the common ratio \(r = \sqrt[3]{-\frac{125}{512}} = -\frac{5}{8}\).

Step 2 ：Next, we can find the first term by dividing the third term by the square of the common ratio. So, the first term \(a = 50 \div \left(-\frac{5}{8}\right)^2 = 50 \div \frac{25}{64} = 50 \times \frac{64}{25} = 128\).

Step 3 ：Finally, we can find the second term by multiplying the first term by the common ratio. So, the second term \(b = 128 \times -\frac{5}{8} = -80\).

Step 4 ：So, the first term is \(\boxed{128}\) and the second term is \(\boxed{-80}\).