Answer:
Explanation:
To find the explicit formula for the given sequence, we can use the recursive formula and keep substituting until we get a general formula.
a₁ = 4
a₂ = a₁ - 4 = 4 - 4 = 0
a₃ = a₂ - 4 = 0 - 4 = -4
a₄ = a₃ - 4 = -4 - 4 = -8
a₅ = a₄ - 4 = -8 - 4 = -12
a₆ = a₅ - 4 = -12 - 4 = -16
We can see that the sequence is decreasing by 4 each time, and we can write the general formula as:
aₙ = 4 - 4(n - 1)
Simplifying the formula, we get:
aₙ = -4n + 8
Therefore, the explicit formula for the given sequence is aₙ = -4n + 8.