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.)

Answer

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Answer

Final Answer: $a_{1} = \boxed{-11}$

Steps

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: $a_{1} = \boxed{-11}$