# 20, 10, 2.5 ?

Sep 13, 2016

See explanation...

#### Explanation:

It is not clear what this question is asking.

Some possibilities:

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What is the next number in the sequence $20 , 10 , 2.5$ ?

Note that $\frac{20}{10} = 2$ and $\frac{10}{2.5} = 4$, so we could expect the next item in the sequence to be:

$\frac{2.5}{6} = 0.41 \overline{6}$

or

$\frac{2.5}{8} = 0.3125$

Since this does not fall into the category of any standard sequence, we could justify all kinds of continuations of the sequence.

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What number is missing in the geometric sequence $20 , 10 , 2.5$?

Note that the sequence:

$20 , 10 , \textcolor{red}{5} , 2.5$

would be a geometric sequence, with each term being half of the preceding one.

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What is the rule and next term of the sequence $20 , 10 , 5 , 2.5$?

Note this assumes that $5$ was missed from the question.

If so, then this looks like a geometric sequence with initial term $20$ and common ratio $\frac{1}{2}$

The formula for a general term would be:

${a}_{n} = 20 \cdot {\left(\frac{1}{2}\right)}^{n - 1}$

and the next term of the sequence would be:

$2.5 \cdot \left(\frac{1}{2}\right) = 1.25$