If a, start subscript, 1, end subscript, equals, 4a 1 =4 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 .
Question
If a, start subscript, 1, end subscript, equals, 4a 1 =4 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 .
Solution
The given sequence is a recursive sequence where each term is found by multiplying the previous term by -3.
Given that a₁ = 4, we can find the next terms as follows:
a₂ = -3 * a₁ = -3 * 4 = -12
a₃ = -3 * a₂ = -3 * -12 = 36
a₄ = -3 * a₃ = -3 * 36 = -108
So, a₄ = -108.
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