Respuesta :
This is a geometric sequence with common ratio r = - 2
r = [tex]\frac{-96}{48}[/tex] = [tex]\frac{192}{-96}[/tex] = [tex]\frac{-384}{192}[/tex] = - 2
Answer:
the sequence is geometric sequence with common ratio (-2).
Option : D is correct.
Step-by-step explanation:
In this question table is given as
n 1 2 3 4 5
f(n) 48 -96 192 -385 768
We have to find out if the sequence is arithmetic or geometric.
For Arithmetic sequence :
Difference should be common in each term of fees.
common difference [tex]d_{1}[/tex] = f(2) - f(1)
= -96 -48 = -144
similarly [tex]d_{2}[/tex] = f(3) - f (2) = 192 + 96 = 288
Here, [tex]d_{1}[/tex] ≠ [tex]d_{2}[/tex] so the sequence is not an arithmetic sequence.
For Geometric sequence :
Ratio should be common in each term of f(n)
Common ratio [tex]r_{1}[/tex] = [tex]\frac{f(2)}{f(1)}=\frac{-96}{48}=(-2)[/tex]
[tex]r_{2}=\frac{f(3)}{f(1)}=\frac{192}{(-96)}=(-2)[/tex]
[tex]r_{1}=r_{2}[/tex]
Therefore, the sequence is geometric sequence with common ratio (-2).
Option : D is correct.
