Respuesta :
Answer:
option a is correct
The next term in the sequence -324, 108, -36, 12,..... is -4
Step-by-step explanation:
In Geometric sequences it follows a pattern where the next term is found by multiplying by a constant i,e common ration(r)
For [tex]a_1, a_2, a_3, a_4, a_5, ....[/tex]
Common ratio(r) = [tex]\frac{a_2}{a_1}=\frac{a_3}{a2} =\frac{a_4}{a_3}...[/tex]
the formula for nth term of this sequence is given by;
[tex]a_n = a_1r^{n-1}[/tex]
Given the sequence: -324, 108, -36, 12,.....
This sequence is a geomtric sequence with common ratio = [tex]-\frac{1}{3}[/tex] and [tex]a_1 = -324[/tex]
Since,
[tex]\frac{a_2}{a_1} = \frac{108}{-324} = -\frac{1}{3}[/tex],
[tex]\frac{a_3}{a_2} = \frac{-36}{108} = -\frac{1}{3}[/tex] and so on..
We have to find the next term in this sequence i.e, [tex]a_5[/tex]
Using nth sequence formula:
[tex]a_5= -324(-\frac{1}{3})^{5-1} = -324(-\frac{1}{3})^{4} = -324 \times \frac{1}{81}= -4[/tex]
Therefore, the next term in the sequence -324, 108, -36, 12,..... is -4