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

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Answer

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

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: $a_{1} = - 11$