Question

Determine whether the sequence converges or diverges. If it converges, give the limit. 72, 18, 9 divided by 2, 9 divided by 8, ...

Answer 1

Sequence converges.

Limit = 96

Explanation:

We are given series 72, 18,
`(9)/(2)`,
`(9)/(4)`, ..........

First we find the common ratio of the given series.

Ratio (r) =
`(18)/(72)`=
`(9/2)/(18)`=
`(9/8)/(9/2)`=
`(1)/(4)`

Here, ratio of the series equal. So, it would be converges.

Now we find the limit of the sequence.

Formula =
`(a)/(1-r)`

where, a=72 and r=
`(1)/(4)`

Limit=
`(72)/(1-1/4)`

Limit =
`(72)/(3/4)`

Limit=96