Question

The 1000th term of the sequence 1,0,-1,1,0,-1,1,0,-1,1....

Answer 1

Answer:

1

Step-by-step explanation:

Given sequence is the recurring of the series 1, 0, -1. Three terms only are occurred in this sequence in the given order.

So to find the nth term of this sequence,

• Consider the remainder got on dividing n by 3.
• If the remainder obtained are 1, 2 or 0, the nth term will be 1, 0 or -1 respectively.

E.g.:

1. 10 divided by 3 leaves remainder 1, so that the 10th term of the sequence is 1.
2. 5 divided by 3 leaves remainder 2, so that 5th term is 0.
3. Also, 9 divided by 3 leaves remainder 0, so that 9th term is -1.

Now let's find the answer to the question.

Given question is to find 1000th term.

Divide 1000 by 3, so that the remainder is 1.

Thus 1000th term of the sequence is 1.