-81, 108, -144, 192, ... which formula can be used to describe the sequence?

Solution:

Given, the sequence is -81, 108, -144, 192,.....

We have to find the formula to describe the sequence.

To find the type of sequence,

Common ratio, r = b/a = c/b = d/c

r = 108/-81 = -144/108 = 192/-144 = -1.333

r = -1.333

So the given sequence is in geometric progression.

The n-th term of a geometric series is given by

\(a_{n}=ar^{n-1}\)

Now, \(a_{n}=-81(-1.3333)^{n-1}\)

Therefore, the formula to describe the sequence is \(a_{n}=-81(-1.3333)^{n-1}\).

-81, 108, -144, 192, ... which formula can be used to describe the sequence?

Summary:

The formula that can be used to describe the sequence -81, 108, -144, 192,..is \(a_{n}=-81(-1.3333)^{n-1}\).