Respuesta :
The eighth term of the given geometric sequence is 256/6561.
What is a geometric progression?
A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: 2/3, 4/9, 8/27...
As we can observe, each successive term of the geometric sequence is 2/3 of the previous one.
Thus, r = 2/3 and a₁ = 2/3.
The formula used to find the nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, [tex]a_8=\frac{2}{3}(\frac{2}{3})^7=\frac{2}{3}^8=\frac{256}{6561}[/tex]
Thus, the eighth term of the given geometric sequence is 256/6561.
To learn more about geometric progression, refer to the link: https://brainly.com/question/15978376
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