Final answer:
A sequence of numbers can indeed be both arithmetic and geometric; the only sequence that is both would be a constant sequence where each term is the same.
Step-by-step explanation:
It is possible for a sequence of numbers to be both arithmetic and geometric. An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio. A sequence that is both must have a common difference and a common ratio that are compatible.
Let's consider a sequence where the first term is 'a' (non-zero) and the common ratio is 'r'. For this sequence to be arithmetic, each term must be the sum of the previous term and a common difference 'd'. This would necessitate that 'ar = a + d'. Simplifying gives 'r = 1 + (d/a)'. For 'd' to be constant, 'a' must not be zero and 'r' cannot change. Therefore, the only way both conditions can be satisfied is if 'r = 1', leading to 'd = 0'. Each term of this type of sequence would be the original term 'a', making it a constant sequence.
Thus, the only sequence that is both arithmetic and geometric is a constant sequence where every term is the same. This logically aligns with the fact that such a sequence can endlessly grow by the same amount (zero in this case), without ever reaching absurdity.