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What is the sequence when taking 3 terms in the fibonacci sequence & multiplying 1st and 3rd together?

After multiplying the first and last terms in the 3 numbers of the fibonacci sequence and subtracting their product by the square of the middle number I get 1 as the difference, but sometimes the subtraction is the opposite, is there a special sequence ?

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06rw9cwhaa profile image
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j0m5deslaa profile image

So fibonacci is: 1 1 2 3 5 8 13 21 34 55 89

The next number is found by taking the sum of the previous two numbers.

So let's try a few:

1 * 2 - 1^2 = 1

1 * 3 -2^2 = -1

2 * 5 - 3^2 = 1

3 * 8 - 5^2 = -1

5 * 13 - 8^2 = 1

8 * 21 - 13^2 = -1

so what are we seeing here? an alternating sequence of positive 1, negative 1, positive 1, negative 1 repeating. so that is your special sequence. maybe your teacher wants you so write it as (-1)^(n+1)