Respuesta :
Answer:
The sequence's fifth term is equal to 7.5.
Step-by-step explanation:
It is given in the question that A sequence is defined recursively using the formula f(n+1)=-0.5f(n) and we need to calculate f(5) if the first term of the sequence is 120.
Firstly,
The definition of a series is given by the formula f (n + 1) = -0.5 f. (n).
Now, what will be f(5) if the sequence's initial term is 120, let's calculate;
Recursively, a series is defined as follows;
=> f(n) = 120 if n = 1, otherwise.
Otherwise,
=> f(n) =-0.5f(n-1) if n > 1.
Now,
=> f(1) = 120
=> f(2) = -0.5f(1) = -0.5(120) = -60
=> f(3) = -0.5f(2) = -0.5(-60) = 30
=> f(4) = -0.5f(3) = -0.5(30) = -15
=> f(5) = -0.5f(4) = -0.5(-15) = 7.5
So, For n > 1, f(n) = (-0.5)(n-1) × 120
Therefore, the sequence's fifth term is equal to 7.5.
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