120, 60, 80, 90, ... [closed]

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I went to the military service day and they had me do an intelligence test. This sequence was one of the last of them:

$$120, 60, 80, 90, \dots$$

Several options came to my mind. In principle there's a rule behind any number you put next, so I guess I'm looking for one of the following:

a. The most natural answer;

b. The most creative answer.

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4 Answers

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Unless I am not wrong..

Explanation $(1)$: $$120\times \frac {1}{2}=60$$ $$120\times \frac {2}{3}=80$$ $$120\times \frac {3}{4}=90$$

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I have an answer, which is, in my opinion, natural and creative:

$$120, 60, 80, 90, 120, 60, 80, 90, 120, 60, 80, 90, \dots.$$

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One more way to do this type of question create two series using alternative terms.

Series 1-

120, 80, ......

We can see difference between them 40.

So next terms are 40, 0, -40, .......

Series 2-

60, 90, ......

We can see series increasing by 30.

So next terms are 120, 150, 180, .......

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you could assume that the sequence is generated like this: $$ a_n=10\cdot6^{1-n} \left[\left(3-\sqrt{15}\right)^n+\left(3+\sqrt{15}\right)^n\right] $$ here is a list of values for $n=0\to20$: $$ 120,60,80,90,103.333,118.333,135.556,155.278,177.87,203.75,233.395,267.353,306.253,350.811,401.854,460.322,527.298,604.018,691.901,792.571,907.888 $$

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