Question

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1?

9.6, –4.8, 2.4, –1.2, 0.6, ...

f(n + 1) = –0.5f(n)
f(n + 1) = 0.5f(n)
f(n + 1) = f(0.5n)
f(n + 1) = f(–0.5n)

Answer 1

Answer:

The recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1 is f(n + 1) = f(n) – 5

Solution:

Given the sequence is:

6 , 1 , - 4 , -9 , -14 , ....

Analyse the given sequence and find the pattern followed

\begin{gathered}First\ term = 6 \\\\Second\ term = 6 - 5 = 1 \\\\Third\ term = 1 - 5 = -4 \\\\Fourth\ term = -4 - 5 = -9 \\\\Fifth\ term = -9 - 5 = -14 \\\\And\ so\ on\end{gathered}

First term=6

Second term=6−5=1

Third term=1−5=−4

Fourth term=−4−5=−9

Fifth term=−9−5=−14

And so on

Thus we can see successive terms are found by subtracting 5 from previous terms

Which can be written as:

f(n + 1) = f(n) - 5f(n+1)=f(n)−5

Where, "n" is the terms location

f(1) = 6 , n \geq 1n≥1

Learn more:

Which recursive formula can be used to generate the sequence shown, where f(1) = 9.6 and n > 1? 9.6, –4.8, 2.4, –1.2, 0.6, ...