Respuesta :
The value of the 10th term of the geometric progression is 30517.578
Based on the information given,
First term = 8
Second term = 20
Common ratio = 20/8 = 2.5
The nth term of a geometric progression is calculated as:
= ar[tex]n[/tex] - 1
The 10th term will then be:
= 8 × (2.5)[tex]9[/tex]
= 8 × 3814.6973
= 30517.578
Therefore, the value of the 10th term of the geometric progression is 30517.578.
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The 10th term of the geometric sequence is: 30,715.578.
In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio q.
The equation for the nth term is:
[tex]a_n = a_1q^{n-1}[/tex]
- In which [tex]a_1[/tex] is the first term.
In this problem:
- The first term is [tex]a_1 = 8[/tex].
- The common ratio is:
[tex]q = \frac{50}{20} = \frac{20}{8} = 2.5[/tex]
Thus, the nth term is given by the following equation:
[tex]a_n = 8(2.5)^{n-1}[/tex]
The 10th term is:
[tex]a_{10} = 8(2.5)^9 = 30517.578[/tex]
The 10th term of the sequence is 30,715.578.
A similar problem is given at https://brainly.com/question/23826475
