Question

Which sequence are geometric? Select three options.

Answer 1

2ND ONE

Explanation:

Answer 2

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

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 = (a_2)/(a_1)`

=
`(-9)/(-2.7)`

=
`(10)/(3)`

Common ratio=
`r = (a_3)/(a_2)`

=
`(-30)/(-9)`

=
`(10)/(3)`

Common ratio=
`r = (a_4)/(a_3)`

=
`(-100)/(-30)`

=
`(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 = (a_2)/(a_1)`

=
`(2.5)/(-1)`

=
`(-5)/(2)`

Common ratio=
`r = (a_3)/(a_2)`

=
`(-6.25)/(2.5)`

=
`(-5)/(2)`

Common ratio=
`r = (a_4)/(a_3)`

=
`(15.625)/(-6.25)`

=
`(-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 = (a_2)/(a_1)`

=
`(9.2)/(9.1)`

=
`1.0109`

Common ratio=
`r = (a_3)/(a_2)`

=
`(9.3)/(9.2)`

=
`1.0108`

Common ratio=
`r = (a_4)/(a_3)`

=
`(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 = (a_2)/(a_1)`

=
`(0.8)/(8)`

=
`0.1`

Common ratio=
`r = (a_3)/(a_2)`

=
`(0.08)/(0.8)`

=
`0.1`

Common ratio=
`r = (a_4)/(a_3)`

=
`(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 = (a_2)/(a_1)`

=
`(-4)/(4)`

=
`-1`

Common ratio=
`r = (a_3)/(a_2)`

=
`(-12)/(-4)`

=
`3`

Common ratio=
`r = (a_4)/(a_3)`

=
`(-20)/(-12)`

=
`(5)/(3)`

Since the common ratios are not equal .

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