Answer:
Sequence converges.
Limit = 96
Step-by-step explanation:
We are given series 72, 18, [tex]\frac{9}{2}[/tex], [tex]\frac{9}{4}[/tex], ..........
First we find the common ratio of the given series.
Ratio (r) = [tex]\frac{18}{72}[/tex]=[tex]\frac{9/2}{18}[/tex]=[tex]\frac{9/8}{9/2}[/tex]=[tex]\frac{1}{4}[/tex]
Here, ratio of the series equal. So, it would be converges.
Now we find the limit of the sequence.
Formula = [tex]\frac{a}{1-r}[/tex]
where, a=72 and r=[tex]\frac{1}{4}[/tex]
Limit=[tex]\frac{72}{1-1/4}[/tex]
Limit = [tex]\frac{72}{3/4}[/tex]
Limit=96
