CPhill

The nth term of the sequence is given by: (-1)^n * (1/2)^(n - 1)

So....the 4th term is given by :    (1/2)(4-1) = (-1)^4 * (1/2)^3   =  1/8

Nope...that's what we're here for....!!!!

Yeah..I did......the post  and the distance the cable is anchored from the post represent the two legs....so we have:

12^2 + 5^2 = h^2    where h is the hypotenuse (the cable length)  ...so...

144 + 25 = h^2

169 = h^2     take the square root of both sides

13 = h =  the cable length in feet

Does that make sense???

The slope is given by :    [ 7 - (-5) ]/ [ 3 - (-1) ] =   [12] / [4] = 3

Each cable forms a right triangle with the post..... the post = 12 feet, the distance the cable is anchored from the post = 5 feet... and the cable length itself =  the hypotenuse = √[12^2 + 5^2] = √169  = 13 feet

And we have 3 of these on each post and 4 posts in total....so...the total length  = (13)(3)(4)  = (13)(12)  = 156 ft

The sum of the first "k" positive integers is given by :   (k)(k + 1)/2

So  (x +)   where x =  28  is just  (28)(29) /2     and  (x+) where x = 27  is just (27)(28)/2 

So we have

(28)(29)/2 -  (270(28)/2        ..... factor out 28/2

[28/2] [ 29 - 27]=

[14] [2]  = 28

And notice that :

1 + 2 + 3 + 4 + 5 + 6 + 7  = 28   

So this equals the sum of the first seven positive integers  =  (7)(8)/2  = 56/2 = (7+)

The anwser is A   ........trapezoids have only one pair of sides that are parallel.....

(28+) - (27+) =

(28)(29)/ 2 - (27)(28)/2  =

(28) [ (29) - (27) ] / 2 =

(28/2) (2) = 28  =  (7)(8)/ 2 =   (7+)   ...so k = 7

According to Wikipedia......the cubit ranged from about 15 to 20.4 inches in length......if we consider the average man to be about 6 feet tall (60 in).....then  60/15  = about 4 cubits