Refer to the sequence 11, 16, 26, 31, 36. explain why the terms in the sequence will continue to alternate between even and odd numbers.

To start to solve this problem, we can look at the common difference. The second term minus the first term is equal to 16 - 11 meaning that the common difference is 5. That means that the common difference is odd. The first number in the sequence is odd. Since the common difference is odd, and since an odd number plus an odd number is odd, that means that the next term will be even, and it is (16). But, since an even (16) + an odd (5) equal an odd, that means that the next term will be even.

This sequence will continue to switch between even and odd numbers because by adding an odd number, you are always changing the parity of the number you are adding it to (no matter if it is even or odd). Continuing the sequence, we see the term 36 + 5 or 41, which is a different parity then 36, showing that this is a continuing pattern.

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