a sequence is defined recursively using the formula (f(n + 1)=-0.5f(n)). if the first term of the sequence…

a sequence is defined recursively using the formula (f(n + 1)=-0.5f(n)). if the first term of the sequence is 120, what is (f(5))?\n-15\n-7.5\n7.5\n15

a sequence is defined recursively using the formula (f(n + 1)=-0.5f(n)). if the first term of the sequence is 120, what is (f(5))?\n-15\n-7.5\n7.5\n15

Answer

Explanation:

Step1: Identify the first - term and the formula

We know (f(1)=120) and (f(n + 1)=-0.5f(n)).

Step2: Find (f(2))

Using the formula with (n = 1), we have (f(2)=-0.5f(1)=-0.5\times120=-60).

Step3: Find (f(3))

Using the formula with (n = 2), we get (f(3)=-0.5f(2)=-0.5\times(-60) = 30).

Step4: Find (f(4))

Using the formula with (n = 3), we have (f(4)=-0.5f(3)=-0.5\times30=-15).

Step5: Find (f(5))

Using the formula with (n = 4), we get (f(5)=-0.5f(4)=-0.5\times(-15)=7.5).

Answer:

7.5