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Is the sequence geometric? If so, identify the common ratio.

2, -4, -16, -36, ...

A. Yes; -2
B. Yes; 2
C. Yes; -3
D. No

Respuesta :

Answer:

No this is not the sequence geometric.

Step-by-step explanation:

Given : 2, -4, -16, -36, ...

To find : Is the sequence geometric? If so, identify the common ratio.

Solution : We have given that 2, -4, -16, -36, ...

In a Geometric Sequence each term is found by multiplying the previous term by a constant.

Geometric Sequence like this:

{a, ar, ar², ar³, ... }

On comparing

2, -4, -16, -36, ...

{ 2 , 2 ×-2, 2×(-2)², 2×(-2)³..

So we get { 2, -4, -8, -16...

Therefore , No this is not the sequence geometric.

Since the quotient between consecutive terms is different, the sequence is not geometric, and the correct option is:

  • D. No

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio.

In this problem, the sequence is: {2, -4, -16, -36, ...}

[tex]-\frac{4}{2} = -2[/tex]

[tex]\frac{-16}{-4} = 4[/tex]

Different quotients, hence not geometric, and option D is correct.

You can learn more about geometric sequences at https://brainly.com/question/11847927

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