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

Question

3 years ago

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1 answer:

Rzqust [24] · Answer 1 · 2022-05-03T17:36:45+03:00

Answer:

Sequence converges.

Limit = 96

Step-by-step explanation:

We are given series 72, 18, $\frac{9}{2}$ , $\frac{9}{4}$ , ..........

First we find the common ratio of the given series.

Ratio (r) = $\frac{18}{72}$ = $\frac{9/2}{18}$ = $\frac{9/8}{9/2}$ = $\frac{1}{4}$

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

Now we find the limit of the sequence.

Formula = $\frac{a}{1-r}$

where, a=72 and r= $\frac{1}{4}$

Limit= $\frac{72}{1-1/4}$

Limit = $\frac{72}{3/4}$

Limit=96