Mathematics, 31.01.2020 12:57 ajayrose

Which sequence are geometric? select three options.

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Answer from: burgoonp

Option 1 , Option 2 and Option 4 are geometric sequence.

Step-by-step explanation:

A sequence is said to be geometric when their exist a common ratio between the consecutive terms.

Option 1) -2.7,-9,-30,-100...

Common ratio= $r = \frac{a_2}{a_1}$

= $\frac{-9}{-2.7}$

= $\frac{10}{3}$

Common ratio= $r = \frac{a_3}{a_2}$

= $\frac{-30}{-9}$

= $\frac{10}{3}$

Common ratio= $r = \frac{a_4}{a_3}$

= $\frac{-100}{-30}$

= $\frac{10}{3}$

Since the common ratios are equal .

Thus -2.7,-9,-30,-100... is a geometric sequence .

Option 2) -1,2.5, -6.25, 15.625 ...

Common ratio= $r = \frac{a_2}{a_1}$

= $\frac{2.5}{-1}$

= $\frac{-5}{2}$

Common ratio= $r = \frac{a_3}{a_2}$

= $\frac{-6.25}{2.5}$

= $\frac{-5}{2}$

Common ratio= $r = \frac{a_4}{a_3}$

= $\frac{15.625}{-6.25}$

= $\frac{-5}{2}$

Since the common ratios are equal .

Thus -1,2.5, -6.25, 15.625 ... is a geometric sequence .

Option 3)9.1,9.2,9.3,9.4....

Common ratio= $r = \frac{a_2}{a_1}$

= $\frac{9.2}{9.1}$

= 1.0109

Common ratio= $r = \frac{a_3}{a_2}$

= $\frac{9.3}{9.2}$

= 1.0108

Common ratio= $r = \frac{a_4}{a_3}$

= $\frac{9.4}{9.3}$

= 1.01075

Since the common ratios are not equal .

Thus 9.1,9.2,9.3,9.4.... is not a geometric sequence .

Option 4) 8,0.8,0.08,0.008 ....

Common ratio= $r = \frac{a_2}{a_1}$

= $\frac{0.8}{8}$

= 0.1

Common ratio= $r = \frac{a_3}{a_2}$

= $\frac{0.08}{0.8}$

= 0.1

Common ratio= $r = \frac{a_4}{a_3}$

= $\frac{0.008}{0.08}$

= 0.1

Since the common ratios are equal .

Thus -18,0.8,0.08,0.008 .... is a geometric sequence .

Option 5) 4,-4,-12,-20...

Common ratio= $r = \frac{a_2}{a_1}$

= $\frac{-4}{4}$

Common ratio= $r = \frac{a_3}{a_2}$

= $\frac{-12}{-4}$

Common ratio= $r = \frac{a_4}{a_3}$

= $\frac{-20}{-12}$

= $\frac{5}{3}$

Since the common ratios are not equal .

Thus 4,-4,-12,-20... is not a geometric sequence .

Answer from: Quest

step-by-step explanation:

Answer from: Quest

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step-by-step explanation:

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Which sequence are geometric? select three options.
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