Find $\mathrm{a}_{1}$ and $\mathrm{S}_{\mathrm{n}}$ for a geometric sequence with the values given below. \[ r=-\frac{1}{2}, a_{n}=\frac{11}{32}, n=6 \] $a_{1}=\square$ (Simplify your answer.)

Step 1 ：We are given a geometric sequence with the common ratio \(r = -\frac{1}{2}\), the sixth term \(a_{n} = \frac{11}{32}\), and \(n = 6\).

Step 2 ：We can find the first term \(a_{1}\) of the geometric sequence using the formula \(a_{1} = \frac{a_{n}}{r^{n-1}}\).

Step 3 ：Substitute the given values into the formula: \(a_{1} = \frac{\frac{11}{32}}{(-\frac{1}{2})^{6-1}}\).

Step 4 ：Simplify the expression to find the value of \(a_{1}\).

Step 5 ：Final Answer: \(a_{1} = \boxed{-11}\)