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: Find the second - term

Given (f(1)=120), and (f(n + 1)=-0.5f(n)). When (n = 1), (f(2)=-0.5\times f(1)=-0.5\times120=-60).

Step2: Find the third - term

When (n = 2), (f(3)=-0.5\times f(2)=-0.5\times(-60) = 30).

Step3: Find the fourth - term

When (n = 3), (f(4)=-0.5\times f(3)=-0.5\times30=-15).

Step4: Find the fifth - term

When (n = 4), (f(5)=-0.5\times f(4)=-0.5\times(-15)=7.5).

Answer:

C. 7.5