ShmoopTube

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Here’s your shmoop du jour, brought to you by decreasing terms.

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No…that would be decreasing terns.

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After the first term, x, each term is determined as half of the previous term plus 4.

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What is the ratio of the fourth term to the first?

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And here are the potential answers…

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For this question, we’re asked to find the ratio of the fourth term to the first.

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Well a ratio is just a relationship between two numbers…

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So to find the ratio between the fourth term and the first, we know we should take the

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value of the fourth term and divide it by the value of the first term…which is given

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to us as x. Now all we have to do is find the value of

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the fourth term. We’re told that after the first term, x,

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each term is determined as half of the previous term plus 4.  

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So the second term will be half of the first term, plus 4…or one-half x plus 4.

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The third term will be half of the second term plus 4 or, simplified, one fourth x plus 6.

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The fourth term will be half of the third term plus 4, or one eighth x plus 7.

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So our ratio is one eighth x plus 7 all over x.

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Change the fraction one-eighth into decimal form, which is 0.125…

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and the correct answer is (C)… 0.125x plus 7 all over x.

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