we conclude that the sequence has 8 terms.
Here we have the geometric sequence:
2/81, 4/27, 8/9, ..., 6912
Notice that each term is equal to 6 times the previous term, such that:
2/81*6 = 4/27
4/27*6 = 8/9
Then the n-th term is equal to:
[tex]a_n = a_1*r^{n-1}[/tex]
Where in this case:
[tex]a_1 = 2/81\\\\r = 6[/tex]
Now we need to find the value of n such that:
[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]
If we apply the natural logarithm to both sides, then:
[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]
Then we conclude that the sequence has 8 terms.
If you want to learn more about geometric sequences:
https://brainly.com/question/1509142
#SPJ1
