Answer :
Answer:
aₙ = -2aₙ₊₁
Step-by-step explanation:
According to the sequence given 16, -8, 4, ...
a1 = 16
a2 = -8
a3 = 4
From the values, we can conclude thst;
a1 = -2(-8)
Since a2 = -8, then;
a1 = -2(a2)
Similarly
a2 = -2(4)
a2 = -2a3
The subsequent sequence are;
a3 = -2a4
The nth term will ne;
aₙ = -2aₙ₊₁
Hence the required recursive function is aₙ = -2aₙ₊₁
The recursive formula for the given sequence is
[tex]a_{n}=-\frac{1}{2} (a_{n-1})\\[/tex]
Given :
The terms of the sequence are 16, -8, 4, ...
Lets find the difference between the terms
[tex]-8-16=-24\\4-(-8)=12[/tex]
There is no common difference. So this is not an arithmetic sequence
Now we check common ratio'
[tex]\frac{-8}{16} =-\frac{1}{2} \\\frac{4}{-8} =-\frac{1}{2} \\[/tex]
The common ratio is -1/2
Now we write recursive formula
[tex]a_{n}=r(a_{n-1})[/tex]
Where 'r' is the common ratio
[tex]a_{n}=r(a_{n-1})\\a_{n}=-\frac{1}{2} (a_{n-1})\\[/tex]
The recursive formula is
[tex]a_{n}=-\frac{1}{2} (a_{n-1})\\[/tex]
Learn more : brainly.com/question/24231459