First of all, observing this series, it is obviously the deformation of the Apponacci series, that is, whenever the number of terms is a multiple of 3, it becomes the inverse of the original number.

Aponatch sequence:

1, 1,2,3,5,8, 13,2 1,34,55,89, 144,233,377,6 10,987, 1597,2584,4 18 1,6765, 10946, 177 1 1,28657,46368 ........

General term formula of Aponazhi sequence;

(As mentioned above, it is also called "Binet.Alfred formula", which is an example of using irrational numbers to represent rational numbers. )

Note: At this time

Back to the topic, because it is the sum of the first n terms, we can observe that an- 1 +an-2+an = 0, (n=3k, k is a positive integer).

It can be roughly regarded as a trinomial cycle, so it is required that the sum of an- 1 or an- 1+an-2 is greater than 1000, and n= 16, an=987, n= 17, an can be obtained by substituting into the formula.

So the answer to this question is 17.

PS: As a junior one topic, it is obviously not required to know the general formula of Fibonacci sequence.

So the questioner's purpose should be to hope that candidates can observe the characteristics of the series, and then list the first twenty or thirty items of the series by enumeration, and get the answer through observation, so the solution to this problem should be enumeration (it is important to say it again).

1, 1,-2,3,5,-8, 13,2 1,-34,55,89,- 144,233,377,-6 10,987, 1597,-2584

Get the answer through the law.

Finally, repeat and list the top 20 items! Say the important thing for the third time! )

The answer is 17.