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

Sequence converges.

Limit = 96

Step-by-step explanation:

We are given series 72, 18, , , ..........

First we find the common ratio of the given series.

Ratio (r) = ===

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

Now we find the limit of the sequence.

Formula =

where, a=72 and r=

Limit=

Limit =

Limit=96

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

72 is the answer to this problem