Final answer:
To find the value of a₅ in the given sequence, we use the recursive formula to calculate the previous terms and then substitute it into the formula. The value of a₅ is -1024.
Step-by-step explanation:
In this problem, we are given the initial value of a (a₁ = 4) and a recursive formula for finding the subsequent terms of the sequence (aₙ = -4aₙ₋₁). We need to find the value of a₅.
Let's use the recursive formula to find the value of a₅:
a₅ = -4a₄
Using the previous terms, we can calculate a₄:
a₄ = -4a₃ = -4(-4a₂) = 16a₂ = 16(4a₁) = 64a₁ = 64(4) = 256
Therefore, a₅ = -4a₄ = -4(256) = -1024.