Question

What is the next term in the sequence below?

Answer 1

A because it is just dividing by -3.

Answer 2

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 $a_1, a_2, a_3, a_4, a_5, ....$

Common ratio(r) = $\frac{a_2}{a_1}=\frac{a_3}{a2} =\frac{a_4}{a_3}...$

the formula for nth term of this sequence is  given by;

$a_n = a_1r^{n-1}$

Given the sequence: -324, 108, -36, 12,.....

This sequence is a geomtric sequence with common ratio = $-\frac{1}{3}$ and $a_1 = -324$

Since,

$\frac{a_2}{a_1} = \frac{108}{-324} = -\frac{1}{3}$,

$\frac{a_3}{a_2} = \frac{-36}{108} = -\frac{1}{3}$ and so on..

We have to find the next term in this sequence i.e, $a_5$

Using nth sequence formula:

$a_5= -324(-\frac{1}{3})^{5-1} = -324(-\frac{1}{3})^{4} = -324 \times \frac{1}{81}= -4$

Therefore, the next term in the sequence -324, 108, -36, 12,..... is -4