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The ROC of Z-transform of the discrete time sequence x(n) = (1/3)ⁿ u(n) - (1/2)ⁿ u(n-1) is

1. 1/3 < |z| < 1/2
2. |z| > 1/2
3. |z| < 1/3
4. 2 < |z| < 3

Correct answer: |z| > 1/2

Solution

The correct option is right because the Z-transform converges for values of |z| greater than the largest pole of the sequence. In this case, the poles are at z = 1/3 and z = 1/2, so the region of convergence (ROC) is outside the largest pole, which is |z| > 1/2.

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