If a, start subscript, 1, end subscript, equals, 8a
1
=8 and a, start subscript, n, end subscript, equals, minus, 3, a, start subscript, n, minus, 1, end subscripta
n
=−3a
n−1
then find the value of a, start subscript, 4, end subscripta
4
.
To find the value of a, we can use the given formulas for a₁ and aₙ:
a₁ = 8aₙ₊₁ = -3aₙ₋₁
We are given aₖ = 8 and aₙ = -3aₙ₋₁. We need to find a₄.
Using the given formula for a₁, we can substitute k = 4 to find a₄:
a₄ = 8a₄₊₁ = -3a₄₋₁
Since a₄₊₁ is the same as a₅ and a₄₋₁ is the same as a₃, we have:
a₅ = -3a₃
Now, we can substitute a₅ and a₃ in the equation:
a₄ = -3a₄₋₁ = -3(-3a₃)
We are given a₃ = 8, so we can substitute this value:
a₄ = -3(-3a₃) = -3(-3(8))
Solving this equation:
a₄ = -3(-3(8)) = -3(-24) = 72
Therefore, the value of a₄ is 72.