Question

Which sequence are geometric? Select three options.

Answer 1

Answer:

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

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

                      = $-1$

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

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

                      = $3$

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 2

Answer:

2ND ONE

Step-by-step explanation: