Question

Find an explicit rule for the nth term of the sequence. 4, -4, 4, -4, ...

Answer 1

`Nth element = 4(-1)^(n-1)`

Explanation:

We see that the sequence goes from +4 to -4 to +4 again and so on.

So, the number value remains the same, but the sign changes.

One way to achieve the prediction is to use the sequence position to determine if the sign will be positive or not.

We notice the negative values are in position 2, 4, 6 and so on. So, we could use (-1)^(n-1), that way for the first element, we'll get (-1)^0, which is equal to 1, so positive, for the second element we'll get (-1)^1, which is -1, so negative, and so on.

The rule would then be:

`Nth element = 4(-1)^(n-1)`