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A day full of math games & activities. Find one near you.
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 \(a_{n}=(5)^{n-1}\times (-5)\)
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