A recursive definition of the given Geometric progression is: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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.
Now,
Given: 2, -4, 8, -16, ...
Here, [tex]r = \frac{-4}{2} = -2[/tex] and a₁ = 2.
Thus, a recursive formula for this geometric progression can be: [tex]a_{n}=a_{n-1}r[/tex], with a₁ = 2 and n > 1.
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