Complete the sequence

Algebra Level 3

Find the number that complete the following sequence:

1 − 2 − 10 − 44 − 160 − 512 − 1504 − ? 1-2 - 10 - 44 - 160 - 512 - 1504 - ?

Hint : Rotating the resolution might help to make the solution converge.


The answer is 4160.

Matthieu Courbaize by Matthieu Courbaize , 24, France

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1 solution

In ordre to solve this, we can use a difference table :

1 2 10 44 160 512 1504
1 8 34 116 352 992
7 26 82 236 640
19 56 154 404
37 98 250
61 152
91 Y
X

A priori the differences don't converge so we can't know for sure the value Y . However, if we manage to find X , then Y is equal to 91 + 91 + X .

But how to find X ? If we rotate the table by 60 ° 60° , we get another sequence : 1 1 - 1 1 - 7 7 - 19 19 - 37 37 - 61 61 - 91 91 - X

We then get a second difference table :

1 1 7 19 37 61 91 X
0 6 12 18 24 30
6 6 6 6 6

This time the differences converge, so we can complete this table :

1 1 7 19 37 61 91 127
0 6 12 18 24 30 36
6 6 6 6 6 6

And therefore, we can complete the first table :

1 2 10 44 160 512 1504 4160
1 8 34 116 352 992 2656
7 26 82 236 640 1664
19 56 154 404 1024
37 98 250 620
61 152 370
91 218
127

Finally, the answer is 4160 .

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