Question

Which of the following is a geometric sequence?

Answer 1

Answer:

  B.  -1, 2, -4, 8

Step-by-step explanation:

The characteristic of a geometric sequence is that adjacent terms have a common ratio. Sequence B is the only one.

  2/-1 = -4/2 = 8/-4 = the common ratio: -2

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Ratios of adjacent terms are different for the other sequences.

Answer 2

Answer:

Option B

Step-by-step explanation:

If a geometric sequence is in the form of a, ar, ar²......... then the condition that should be fulfilled is $\frac{A_{2}}{A_{1}}$ = $\frac{A_{3}}{A_{2}}$

= $\frac{ar}{a}$ = r

For Option A ⇒

$\frac{A_{2}}{A_{1}}$ = $\frac{-3}{-1}$ = 3

$\frac{A_{3}}{A_{2}}$ = $\frac{9}{-3}$ = -3

and 3 ≠ -3

So its not a geometric sequence.

Option B ⇒

$\frac{A_{2}}{A_{1}}$ = $\frac{2}{-1}$ = -2

$\frac{A_{3}}{A_{2}}$ = $\frac{-4}{2}$ = -2

-2 = -2

Therefore, option B is a geometric sequence.

Option C ⇒

$\frac{A_{2}}{A_{1}}$ = $\frac{4}{1}$

$\frac{A_{3}}{A_{2}}$ = $\frac{9}{4}$ = 2.25

and 4 ≠ 2.25

So it is not a geometric equation.

Option D ⇒

$\frac{A_{2}}{A_{1}}$ = $\frac{3}{1}$ = 3

$\frac{A_{3}}{A_{2}}$ = $\frac{5}{3}$ =

3 ≠ $\frac{5}{3}$

Therefore, it's not a geometric sequence.

Option B is the answer.