# What is the tenth term of the geometric sequence with #a_1 =4# and #r = 1/2#?

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To find the tenth term of a geometric sequence with (a_1 = 4) and (r = \frac{1}{2}), use the formula for the nth term of a geometric sequence: (a_n = a_1 \cdot r^{(n-1)}). Plugging in the given values, we get (a_{10} = 4 \cdot (\frac{1}{2})^{(10-1)} = 4 \cdot (\frac{1}{2})^9 = 4 \cdot (\frac{1}{512}) = \frac{4}{512} = \frac{1}{128}). Therefore, the tenth term of the sequence is (\frac{1}{128}).

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