For the following geometric sequence find the 5th term in the sequence. {0.125, -0.25, 0.5, ...}

Solution:

Given, the series 0.125, -0.25, 0.5,.... is in geometric progression.

The n-th term of the geometric sequence is calculated by \(a_{n}=ar^{(n-1)}\)

Here, a = 0.125

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

r = -0.25/0.125 = 0.5/-0.25

r = 2

Now, the fifth term of the sequence is \(a_{5}=ar^{(5-1)}\)

\(a_{5}=(0.125)(2)^{4}\)

\(a_{5}=2\)

Therefore, the fifth term of the sequence is 2.

For the following geometric sequence find the 5th term in the sequence. {0.125, -0.25, 0.5, ...}

Summary:

For the following geometric sequence {0.125, -0.25, 0.5, ...}, the 5th term in the sequence is 2.