Respuesta :
Answer:
r = 5
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r is the common ratio
Here a₁ = 1 and a₅ = 625, thus
1 × [tex]r^{4}[/tex] = 625 , so
r = [tex]\sqrt[4]{625}[/tex] = 5
The common ratio of the geometric sequence is 5 if the geometric sequence for which a1=1 and a5=625 the answer is 5.
What is a sequence?
It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a geometric sequence for which:
The first term a1 = 1
and fifth term:
a5 = 625
As we know, the geometric sequence follows a certain arithmetic rule of multiplication.
The nth term of the geometric sequence is:
a(n) = arⁿ⁻¹
a1 = a = 1
a5 = ar⁵⁻¹ = 625
Take the ratios:
a/ar⁵⁻¹ = 1/625
r is the common ratio.
1/r⁴ = 1/625
r⁴ = 625
r = 5
The common ratio is 5.
Thus, the common ratio of the geometric sequence is 5 if the geometric sequence for which a1=1 and a5=625 the answer is 5.
Learn more about the sequence here:
brainly.com/question/21961097
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