We can examine the pattern and derive the general formula to find the explicit formula for the given recursive sequence.
The recursive formula is as follows:
a₁ = 16
aₙ = -(1/4) * aₙ₋₁
Let's analyze the first few terms of the sequence to identify a pattern:
a₁ = 16
a₂ = -(1/4) * a₁ = -(1/4) * 16 = -4
a₃ = -(1/4) * a₂ = -(1/4) * (-4) = 1
a₄ = -(1/4) * a₃ = -(1/4) * 1 = -1/4
a₅ = -(1/4) * a₄ = -(1/4) * (-1/4) = 1/16
From the pattern observed, we can see that the sign alternates between positive and negative, and the denominator of the fraction is a power of 4.
Based on this pattern, we can define the explicit formula for the sequence:
aₙ = (-1)^(n-1) * (1/4)^(n-1) * 16
Therefore, the explicit formula for the given recursive sequence is
aₙ = (-1)^(n-1) * (1/4)^(n-1) * 16.