If the first term of the sequence is 120, then f(5) will be 7.5
What is recursively sequence?
- In mathematics and theoretical computer science, a constant-recursive sequence is an infinite sequence of numbers satisfying a linear recurrence relation: each number in the sequence is equal to a fixed linear combination of one or more of its immediate predecessors.
- A recursive sequence is a sequence of numbers formed by using previous terms to find the next terms, such as the Fibonacci sequence.
How to solve this problem?
The steps are as follow:
- From the given conditions We knew the sequence is defined by the formula f(n + 1) = - 0.5f(n) and we know f(1) = 120
- So f(1 + 1) = f(2) = - 0.5f(1) = - 0.5 * 120 = f(2) = - 60
- Then f(2+1) = f(3) = -0,5 f(2) = -0,5x-60 f(3)=30
- f(3 + 1) = f(4) = - 0.5f(3) = - 0.5 * 30 = f(4)= -15
- f(4 + 1) = f(5) = - 0.5f(4) = - 0.5x - 15 = f(5) = 7.5
- So, f(5) = 7.5
So if the first term of the sequence is 120, then f(5) will be 7.5
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