Practice your math skills regularly by solving the Math Madness Quiz Questions and keep them strong enough to ace your college admissions exams!

## The 7th term in a geometric sequence is 1458.  The first term in the sequence is 2.  What is the 10th term?

A) 13,122

B) 118,098

C) 4,374

D) 39,366

E) None of the above

Stay tuned next week for the solution!

Solution for the last Math Madness question; 4/22/19:  C)  14

1)  First step is to solve for X

You are given the measurements of the perimeter of the yard as x+10, x+10, x-5, x-5; and the total of the perimeter, which is 90 feet.  From this, you can derive the formula

(x+10) + (x+10) + (x-5) + (x-5) = 90             or             2(x+10) + 2(x-5) = 90

Simplify

x + 10 + x + 10 + x – 5 + x – 5 = 90            or              2x + 20 + 2x – 10 = 90

4x + 10 = 90                                                    or                   4x + 10 = 90

-10   -10                                                                                    -10   -10

4x = 80                                                           and                        4x = 80

/4     /4                                                                                           /4     /4

x = 20                                                                                                  x = 20

2) Now you can solve for the sides:

The longer sides (qty of 2)                                                             The shorter sides (qty 2)

x + 10       substitute 20 for x                                                          x – 5            substitute 20 for x

20 + 10                                                                                           20 – 5

30                                                                                                     15

The long sides are 30’ long                                                          The shorter sides are 15’ long

Now that you know the length of the sides, and knowing that each tree needs 5’ of space (2.5’ radius = 5’ diameter), you can divide the length of each side to see how many trees would fit on each side of the yard.

The long sides                                                                                                   The short sides

30 feet / 5 feet = 6                                                                                          15 feet / 5 feet = 3

6 trees can fit along the back wall                                                       3 trees can fit on the side walls

Before you jump to conclusions and add up 6 + 6 + 3 + 3, consider the corner of the yards.  The corner trees are on both a long wall and a short wall. Each wall would have 2 of its trees on double walls.  Therefore, take 2 trees out from each side and label them as the corner trees.  There are a total of 4 corner trees.

The long sides:  6 – 2 = 4.  The short sides:  3 – 2 = 1.  And the corners: 4.  Add these all together, remember there are 2 of each side.  (Draw a diagram for a visual)

4 + 4 + 1 + 1 + 4 (the corner trees)

14 trees in total to surround the backyard.