Find an explicit rule for the nth term of the sequence. 2, -8, 32, -128, …

Solution:

Given, the sequence is 2, -8, 32, -128, ….

We have to find an explicit rule for the nth term of the sequence.

First finding the type of sequence,

First term, a = 2

Common ratio, r = -8/2 = 32/-8 = -128/32 = -4

Thus, the given sequence is in geometric progression.

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,

\(a_{n}=(2)(-4)^{n-1}\)

\(a_{n}=(-4)^{n-1}\times (2)\)

Therefore, the explicit rule for the sequence is \(a_{n}=(-4)^{n-1}\times (2)\).

Find an explicit rule for the nth term of the sequence. 2, -8, 32, -128, …

Summary:

An explicit rule for the nth term of the sequence. 2, -8, 32, -128,…is \(a_{n}=(-4)^{n-1}\times (2)\).