Respuesta :
All the terms of the given geometric sequence are integers for [tex]n\geq 1[/tex].
What is a geometric sequence?
- A geometric sequence is a sequence of numbers where the ratio of two consecutive numbers is constant. This ratio is also known as the common ratio of the geometric sequence.
- For example, [tex]2,4,8,16,...[/tex] is a geometric sequence as [tex]\frac{4}{2}=\frac{8}{4}=\frac{16}{8}=2[/tex] i.e., the ratio of any two consecutive numbers is constant. Here, the common ratio is [tex]r=2[/tex].
- The nth term of a geometric sequence whose first term is [tex]a[/tex] and the common ratio is [tex]r[/tex] is given by the formula [tex]a_n=ar^{n-1}[/tex].
Given that the first term of a geometric sequence is [tex]a=a_1=3[/tex] and the common ratio is [tex]r=-1[/tex].
So, the nth term of the sequence is given by: [tex]a_n=ar^{n-1}=3\times(-1)^{n-1}=\left \{ {{3\hspace{0.5cm}\text{if n is odd}} \atop {-3\hspace{0.5cm}\text{if n is even}}} \right.[/tex]
Thus, all the terms of the given geometric sequence are integers for [tex]n\geq 1[/tex].
To learn more about the geometric sequence, refer: https://brainly.com/question/1509142
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