Identify the Sequence 0 , 2 , 0 , 2 , 0 , 2

Problem

0,2,0,2,0,2,…

Solution

1. Identify the pattern of the sequence by observing the terms. The sequence alternates between 0 and 2

2. Determine the characteristics of the sequence. Since the terms repeat in a cycle, it is a periodic or oscillating sequence.

3. Find a general formula for the nth term (a_n) starting from n=1 The sequence can be represented using a trigonometric function or a power of −1

4. Apply the formula for an alternating sequence. Using the form (a_n)=1+(−1)n we test the values: for n=1 1 - 1 = 0;ƒ*o*r=2, + 1 = 2$.

Final Answer

(a_n)=1+(−1)n

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