The sequence x_n={1, 2, 3, 4, 5, 5, 6, ...} is .......... and ............. sequence.1 pointan increasing and unboundeda non-decreasing and unboundeda decreasing and unboundedan increasing and bounded

The sequence x_n={1, 2, 3, 4, 5, 5, 6, ...} is a non-decreasing and unbounded sequence.

Here's why:

1. Non-decreasing: In a non-decreasing sequence, each term is either greater than or equal to the preceding term. In the given sequence, you can see that no term is less than the term before it. For example, 2 is greater than 1, 3 is greater than 2, 4 is greater than 3, 5 is equal to 5, and 6 is greater than 5. Therefore, the sequence is non-decreasing.

2. Unbounded: A sequence is said to be unbounded if it does not have an upper or lower limit. In this case, the sequence does not have an upper limit because it continues indefinitely (as indicated by the ellipsis), and each term is greater than or equal to the previous term. Therefore, the sequence is unbounded.