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8 0 9 24 10 120 11 336 12 __ ?

Hint:

It is logical.

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5 Answers 5

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The answer is:

720

Reason:

The first even term is 24*0, second is 24*1, third is 24*5, fourth is 24*14, and lastly we have 24*30. So we have 0, 1, 5, 14, 30. The difference between these numbers are the first 4 squares; 1², 2², 3², 4².

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  • $\begingroup$ [24, 120, 336, 720] all of them are completely divisible by [2,3,4,6,8,12,24].. $\endgroup$
    – user64002
    Commented Nov 24, 2019 at 9:42
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Is the answer 720 because there is an alternating pattern- the pattern of the even terms is like so +(6x4), +(6+18)x4), +(6+18+30)x4), +(6+18+30+42)x4) A pattern of 18,30,42 which is +12,+12

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    $\begingroup$ Well? Is it right? $\endgroup$
    – PDT
    Commented Nov 23, 2019 at 22:17
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Good to have a different way of answering. My logic is little bit easy:

8 $\hspace{2cm}$9$\hspace{2cm}$10$\hspace{2cm}$11$\hspace{2cm}$12

$\hspace{1cm}$0 $\hspace{2cm}$24$\hspace{2cm}$120$\hspace{2cm}$336$\hspace{2cm}$___?

$\hspace{0.4cm}$$1^3-1$$\hspace{1cm}$ $3^3-3$ $\hspace{1.2cm}$ $5^3-5$ $\hspace{1cm}$ $7^3-7$ $\hspace{1.2cm}$ $9^3-9$

Next term is:

$$9^3-9 = 720$$

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Somebody has already solved it, but here is the detail explanation again:

8           9           10          11         12   

   0             24         120         336

    24 * 0        24 * 1     24 * 5      24 * 14

         0             1          5           14

                1          4           9                     

                1^2        2^2         3^2      ->   4^2

                1     +    4     +     9      +      16    =   30   


Result:  24 * 30 = 720                         
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another (and one of the shortest) reasoning for 720: the even terms are the square pyramidal numbers multiplied by 24.

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