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

Answer 1

#a_(10)=1/128#

The #color(blue)"nth term of a geometric sequence"# is.

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(a_n=ar^(n-1))color(white)(2/2)|)))# where a is the first term and r, the common ratio.

#rArra_(10)=4xx(1/2)^9#

#color(white)(rArra_(10))=4xx1/512#

#color(white)(rArra_(10))=1/128#

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Answer 2

Ariana Alvarez

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.