Question

What is the next term in the following sequence?54, -18, 6, ...-232-3

Answer 1

What is the next term in the following sequence?

54, -18, 6, :

common ratio: r = T2/T1

`\begin{gathered} r=(T_2)/(T_1)=(T_3)/(T_2) \\ r=-(18)/(54)=(6)/(-18)=-(1)/(3) \end{gathered}`

The next term will be

`\begin{gathered} r=(T_4)/(T_3) \\ -(1)/(3)=(x)/(6) \\ 3x=-6 \\ x=-(6)/(3) \\ x=-2 \end{gathered}`

Therefore the next term in the following sequence = -2

Hence the correct value = -2