What is the minimum period of the discrete sequence

Question

Question

This question was previously asked in

VSSC ISRO Technical Assistant Electronics 14 July 2021 Official Paper

Answer 1

Fundamental period:

The smallest possible value of a period is called the fundamental period of a given sequence.

than fundamental period (N) of x[n] is given as,

where k is an integer.

Given sequence is:

then period for is

then the period for is

overall period for x[n] is given as

N = LCM (N₁,N₂)

N = LCM (4,6)

N = 12