Using a geometric sequence, it is found that the possible values of the 6th term of the sequence are -70 and 70.
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
The nth term can also be written as a function of the mth term, as follows:
[tex]a_m = a_1q^{n-m}[/tex]
In this problem, considering that we have the 5th and the 7th term, we have that:
[tex]a_7 = a_5q^2[/tex]
Since [tex]a_5 = 140, a_7 = 35[/tex]:
[tex]q^2 = \frac{a_5}{a_7}[/tex]
[tex]q^2 = \frac{35}{150}[/tex]
[tex]q^2 = \frac{1}{4}[/tex]
[tex]q = \pm \frac{1}{2}[/tex]
[tex]\pm \frac{1}{2}[/tex] of 140 is [tex]\pm 70[/tex], hence the possible values of the 6th term of the sequence are -70 and 70.
More can be learned about geometric sequences at https://brainly.com/question/11847927
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