Question

Which term of the sequence; 256, -64, 16, -4.............is equal to 1/4090?

Answer 1

Answer on Question #77136 – Math – Algebra

Question

Which term of the sequence; 256, -64, 16, -4...is equal to 1/4096?

Solution

Each term could be calculated as

$B_n = B_1 q^{n-1}$, where $B$ – initial term, and $q$ – common ratio;

$$q^{n-1} = \frac{B_n}{B_1} = \frac{1}{4096 \times 256} = \frac{1}{1048576}$$ $$q^1 = \frac{B_2}{B_1} = \frac{-64}{256} = -\frac{1}{4}$$ $$n-1 = \log_{-\frac{1}{4}} \frac{1}{1048576}$$ $$n-1 = 10$$ $$n = 11$$

Answer:

1/4096 is the $11^{\text{th}}$ term of the sequence.

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