The nth element of a series is represented as X_n = (-1)^nX_{n-1} If X_0 = x and x > 0, then which of the following is always true?

Question 20

The nth element of a series is represented as

$$X_n = (-1)^nX_{n-1}$$
If $$X_0 = x$$ and $$x > 0$$, then which of the following is always true?

Solution

Let x = 1, so, $$X_0$$ = 1
$$X_1$$ = -1
$$X_2$$ = -1
$$X_3$$ = 1
$$X_4$$ = 1
$$X_5$$ = -1
$$X_6$$ = -1
So, $$X_n$$ need not be positive when n is even, $$X_n$$ need not be positive when n is odd, $$X_n$$ need not be negative when n is even. So, none of the first three options are correct.

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The nth element of a series is represented as $$X_n = (-1)^nX_{n-1}$$ If $$X_0 = x$$ and $$x > 0$$, then which of the following is always true?

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The nth element of a series is represented as

$$X_n = (-1)^nX_{n-1}$$
If $$X_0 = x$$ and $$x > 0$$, then which of the following is always true?