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Sagot :
The 6th term of the geometric sequence is -1/2.
Here we have to find the a6the term of the geometric sequence.
Data given:
The series = 512/243, -128/81, 32/27.....
The formula to find the nth term of the geometric sequence:
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where [tex]a_{n}[/tex] = nth term of the sequence
a = first term of the sequence
r = common ratio
common ratio(r) = -128/ 81 ÷ 512/ 243
= -128/81 × 243/512
= -3/4
Now we have to find the 6th term of the series.
[tex]a_{6}[/tex] = 512/ 243 (-3/4[tex])^{6-1}[/tex]
= 512/243 (-3/4[tex])^{5}[/tex]
= 512/243 × 243/1024
= -512/1024
= -1/2
Therefore the 6th term is -1/2.
To know more about the geometric sequence refer to the link given below:
https://brainly.com/question/24643676
#SPJ4
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