Find an explicit rule for the nth term of the sequence. -5, -25, -125, -625, …

Solution:

Given, the sequence is -5, -25, -125, -625,.......

We observe the term is in geometric progression.

First term, a = -5

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

r = -25/-5 = -125/-25 = -625/-125 = 5

So, r = 5

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,

\(a_{n} = (-5)(5)^{n-1}\)

\(a_{n} = (5)^{n-1}\times (-5)\)

Therefore, the explicit rule for the sequence is \(a_{n} = (5)^{n-1}\times (-5)\)

Find an explicit rule for the nth term of the sequence. -5, -25, -125, -625, …

Summary:

An explicit rule for the nth term of the sequence. -5, -25, -125, -625, …is  \(a_{n}=(5)^{n-1}\times (-5)\)