hi,

(b) for the height of structure,

if the structure no. is odd, you get the height by taking the structure no. + 1, and then divide by 2. Take this result and multiply by 3.

for eg. for structure 1, the height is (1 + 1) / 2 x 3 = 3

for structure 5, it is (5 + 1) / 2 x 3 = 6

so for structure 119, the height will be (119 + 1) / 2 x 3 = 180

[though not asked, you may notice that for structure no. that are even, it is simply structure no. divide by 2, then multiply by 3]

(c) For the no. of rods used, notice that for structure 3, you add 8 to that of structure 2; then you go on by adding 5, and then add 8, then add 5, then add 8, etc.

struct. no.......no. of rods

...2....................20

...3...................20 + 8

...4...................28 + 5

...5...................33 + 8

...6...................41 + 5

...7...................46 + 8, etc.

that means, when you move through odd no. structures, you keep adding 13, as

struct. no.......no. of rods

...3...................20 + 8.....................= 2 x 13 + 2 = (3 + 1)/2 x 13 + 2

...5...................33 + 8 = 28 + 13.....= 3 x 13 + 2 = (5 + 1)/2 x 13 + 2

...7...................46 + 8 = 41 + 13.....= 4 x 13 + 2 = (7 + 1)/2 x 13 + 2

so, the trick is now to figure out the relationship between the structure no. and the no. that you need to multiply by 13, and that is structure no. + 1, then divide by 2.

So, for structure 119, the no. of rods = (119 + 1)/2 x 13 + 2 = 120/2 x 13 + 2

= 60 x 13 + 2 = 780 + 2 = **782**

Hope this helps!