Explanation

To find the missing term in the sequence, let's examine the pattern:

1/3, 1/8, ?, 2/3

First, notice the denominators: 3, 8, ?, 3.

The denominators don't seem to follow a straightforward arithmetic or geometric progression. Let's look at the numerators:

1, 1, ?, 2

The numerators seem to increase by 1 each time.

If we consider that the numerators increase by 1 and the denominators are not following a clear pattern, we could assume a pattern where the numerators increase by 1 every two terms.

Following this pattern, the missing term should have a numerator of 1, and since it's the second term after 1/8, the denominator should be 5 (since 3 + 2 = 5).

So, the missing term is 1/5.

Therefore, the completed series is:

1/3, 1/8, 1/5, 2/3

Explanation

To find the pattern, let's break down the given series:

13, 32, 24, 43, 35, ?, 46, 65, 57, 76

Looking at the differences between consecutive numbers:

32 - 13 = 19

24 - 32 = -8

43 - 24 = 19

35 - 43 = -8

So, it seems like there's an alternating pattern of adding and subtracting 8 and 19 between the numbers.

Following this pattern:

35 + 19 = 54

54 - 8 = 46

So, the missing number is 54.

Thus, the completed series is:

13, 32, 24, 43, 35, 54, 46, 65, 57, 76