Question

Determine if the sequence is geometric. If it is, find the common ratio. −1, 6, −36, 216, ..

Answer 1

Answer:

Geometric Sequence

Step-by-step explanation:

First Option for solutions:

216/-36= -6

-36/6= -6

6/-1= -6

therefore the ratio was -6

second option for solutions:

-by formula an=a1rn-1

note: in a1 the 1 is the first term and the n-1 was exponent...

an=a1rn-1

216= -1r⁴-¹

216= -1r³

216/-1= -1/-1r³

-216=r³

³√-216= ³√r³

-6 =r

therefore the ratio was -6

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Answer 2

Hint:

A sequence of the numbers $a_{1},a_{2},a_{3},a_{4},...$ is said to be geometric if

$\quad \dfrac{a_{2}}{a_{1}}=\dfrac{a_{3}}{a_{2}}=\dfrac{a_{4}}{a_{3}}=...$

Step-by-step Explanation:

The given sequence is

$\quad -1,6,-36,216,...$

Let us consider:

$\quad a_{1}=-1,a_{2}=6,a_{3}=-36,a_{4}=216,...$

Now $\dfrac{a_{2}}{a_{1}}=\dfrac{6}{-1}=-6$,

$\quad\dfrac{a_{3}}{a_{2}}=\dfrac{-36}{6}=-6$,

$\quad\dfrac{a_{4}}{a_{3}}=\dfrac{216}{-36}=-6$, ...

We have: $\quad \dfrac{a_{2}}{a_{1}}=\dfrac{a_{3}}{a_{2}}=\dfrac{a_{4}}{a_{3}}=...=-6$

Final Answer:

Thus the given sequence is geometric and the common ratio is $(-6)$.

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