Final answer:
The given sequence can either be arithmetic with a common difference of -14, resulting in the next three terms of 0, -14, and -28; or it can be geometric with a common ratio of 0.5, leading to the next terms being 7, 3.5, and 1.75. Both sequences are infinite. A sequence that is neither arithmetic nor geometric follows a different pattern.
Step-by-step explanation:
The sequence provided, 28, 14,... can be either arithmetic or geometric depending on the pattern it follows. If it is an arithmetic sequence, the common difference can be found by subtracting any term in the sequence from the next one. In this case, 14 minus 28 gives a common difference of -14. Therefore, the next three terms in the sequence, decreasing by 14 each time, would be 0, -14, -28. An arithmetic sequence is infinite; it will keep on going indefinitely no matter how large or how small the terms get.
If we consider the sequence to be geometric, the common ratio is found by dividing any term in the sequence by the term before it, which in this case is 14 divided by 28, giving a common ratio of 0.5. The next three terms would be found by multiplying each term by 0.5, resulting in 7, 3.5, 1.75. A geometric sequence also continues indefinitely and is thus considered infinite.
To write the next three terms of a sequence that is neither arithmetic nor geometric, you can't use a single common difference or ratio. Instead, you might use a different rule or pattern. For example, you could add increasing even numbers, such as adding 14, then 16, then 18, resulting in the terms 42, 58, 76, which do not fit any of these options provided.