Question

Is the sequence - 1,6,-36,216 geometric?

Answer 1

Yes it is

Explanation:

For geometric sequences, the ratios between two adjacent terms have to be the same

SO using the terms in your geometric sequence,

`6/-1 = -36/6 = 216/-36 = -6`

Since the ratios are all the same, then yes it is a geometric sequence

Answer 2

Yes, with the formula being : `T_n=1/6(-6)^n`

Explanation:

It is a geometric sequence, as you can see, the term that follows is `(-6)` multiplied by the previous term.

Hence, we can derive a formula for the nth term of this sequence:

`T_n=-1(-6)^(n-1)`
`color(white)(T_n)=1/6(-6)^n`

Answer 3

`"yes"`

Explanation:

`"for the sequence to be geometric there must be a"`
`color(blue)"common ratio r ""between the terms"`

`•color(white)(x)r=a_2/a_1=a_3/a_2=....=a_n/a_(n-1)`

`"here "a_2/a_1=6/(-1)=-6`

`a_3/a_2=(-36)/6=-6`

`a_4/a_3=216/(-36)=-6`

`"a common ratio exists between the terms hence sequence"`
`"is geometric"`