The Solution:
A geometric sequence is said to converge if the value of the modulus of r is less than one, that is, when |r| < 1, the series converges. But when |r| ≥ 1, the series/sequence diverges.
Clearly, we have that:
[tex]\begin{gathered} \text{ r=3 does not converge } \\ \text{ So, option A does not converge.} \end{gathered}[/tex]
[Option C] converges since
[tex]|r|=\frac{3}{5}<1[/tex]
Similarly,
[Option E] converges since
[tex]|r|=-\frac{1}{6}<1[/tex]
Therefore, the correct answer is [option C and E]
