Answer:nth term = 0 + ((n-1) mod 2) * (2/3)
Step-by-step explanation:
Given : 0, 2/3, 0, 2/3
we can use the following formula:
nth term = a + (n-1)d
where a = first term of the sequence, d =common difference between consecutive terms.
In this case, a = 0 and d = 2/3 - 0 = 2/3. Since the sequence has a period of 2, we can write:
nth term = 0 + ((n-1) mod 2) * (2/3)
where (n-1) mod 2 is the remainder when (n-1) is divided by 2. This expression gives us 0 for even values of (n-1) and 2/3 for odd values of (n-1), which matches the given sequence.
Therefore, a formula for the nth term of the sequence is:
nth term = 0 + ((n-1) mod 2) * (2/3)