The given sequence is geometric, with a common ratio of -5.
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 2, -10, 50, -250, ....
We can observe here: [tex]\frac{-10}{2}=\frac{50}{-10}=\frac{-250}{50} = -5[/tex], hence following the condition required for a sequence to be geometric.
Hence, The given sequence is geometric, with a common ratio of -5.
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