Question

I need help with all three questions please. I am just Stuck.

Answer 1

`p_(o) = 6`,
`r = 2`,
`p_(12) = 24576`.

Explanation:

The value of
`p_(o)` is the first value of the geometric series, that is,
`p_(o) = 6`.

If the series represents a geometric sequence, then
`r` must be constant for every consecutive pair of elements, that is:

`r_(1) = (p_(1))/(p_(o)) = (12)/(6) = 2`

`r_(2) = (p_(2))/(p_(1)) = (24)/(12) = 2`

`r_(3) = (p_(3))/(p_(2)) = (48)/(24) = 2`

Since
`r_(1) = r_(2) = r_(3) = 2`,
`r = 2`.

The geometric sequence can be represented by the following formula:

`p_(n) = p_(o)\cdot r^(n)`, for
`n \in \mathbb{N}`

The 12th element of the geometric sequence is: (
`p_(o) = 6`,
`r = 2`,
`n = 12`)

`p_(12) = 6\cdot 2^(12)`

`p_(12) = 24576`