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please someone help

What is the common ratio of the sequence?

-2, 6, -18, 54,...

−3
−2
3
8

Sagot :

Answer:

ratio = -3

Step-by-step explanation:

To find the common ratio of the sequence, we use this geometric sequence formula:

[tex]\boxed{U_n=U_1\cdot r^{n-1}}[/tex]

where:

  • [tex]U_n=\texttt{the n-th term}[/tex]
  • [tex]U_1=\texttt{the first term}[/tex]
  • [tex]r=\texttt{ratio}[/tex]

To find the ratio, we can pick any pair of the consecutive terms to substitute to the formula. The easiest pair would be U₁ and U₂.

[tex]\begin{aligned}U_2&=U_1\cdot r^{2-1}\\6&=-2\cdot r^{2-1}\\r&=6\div -2\\r&=\bf -3\end{aligned}[/tex]

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