Find the 13th term of the following geometric sequence.
6, 18, 54, 162, ...

Step-by-step explanation:

the ratio is always 3. This is called the common ratio. If the first term of the sequence is a and the common ratio is r, then the geometric sequence can be written as a, ar, ar2, ar3, …, arn−1, … which has nth term arn−1.

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