Find an explicit rule for the nth term of the sequence. 3, -12, 48, -192, …

Solution:

Given, the sequence is 3, -12, 48, -192,.......

We observe the term is in geometric progression

First term, a = 3

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

r = -12/3 = 48/-12 = -192/48 = -4

So, r = -4

The n-th term of the geometric sequence is given by the formula

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

Substituting the values of a and r,

\(a_{n}=3(-4)^{n-1}\)

\(a_{n}=(-4)^{n-1}\times 3\)

Therefore, the explicit rule for the sequence is \(a_{n}=(-4)^{n-1}\times 3\).

Find an explicit rule for the nth term of the sequence. 3, -12, 48, -192, …

Summary:

An explicit rule for the nth term of the sequence. 3, -12, 48, -192, …is  \(a_{n}=(-4)^{n-1}\times 3\).