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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.

  • 0
    This sequence is too short to do much with. Here, nothing obvious leaps to mind. Are you sure it isn't $180$? At least then $a_{2n}=\frac {a_{2n-1}}2$ which is something. – 2017-01-19
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    Have a look at http://math.stackexchange.com/a/1790666/44121 – 2017-01-19
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    $0$ is a possible and reasonable answer, since it is the value at $x=5$ of the interpolating polynomial $350 - 345 x + 130 x^2 - 15 x^3$. – 2017-01-19
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    $120\times 60 = 80\times 90$ .... okay,so I'm still thinking. – 2017-01-19
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    Most likely $96.$ – 2017-01-19

4 Answers 4

7

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 will keep adding as and when something strikes me. – 2017-01-19
1

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

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

0

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, .......

0

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 $n=0\to20$: $$ 120,60,80,90,103.333,118.333,135.556,155.278,177.87,203.75,233.395,267.353,306.253,350.811,401.854,460.322,527.298,604.018,691.901,792.571,907.888 $$