Solution
What is the next term in the following sequence?
54, -18, 6, :
common ratio: r = T2/T1
[tex]\begin{gathered} r=\frac{T_2}{T_1}=\frac{T_3}{T_2} \\ r=-\frac{18}{54}=\frac{6}{-18}=-\frac{1}{3} \end{gathered}[/tex]The next term will be
[tex]\begin{gathered} r=\frac{T_4}{T_3} \\ -\frac{1}{3}=\frac{x}{6} \\ 3x=-6 \\ x=-\frac{6}{3} \\ x=-2 \end{gathered}[/tex]Therefore the next term in the following sequence = -2
Hence the correct value = -2
