Firstly, I acquired a C in maths GCSE over 10 years ago and have never needed to look at problems like I have posted since. Secondly I have been shoved onto a HNC Mechanical Engineering course through my employers, which I am not arguing about I mean its a good qual but I was always going to struggle with the maths, hence using this forum! However I am determined to pass and have fully applied myself!

Since I first posted I have had 2 lessons and Ive a much better idea of how to solve these problems:

8 a. How many weeks will it take to reach maximum output?

I found variables; a = 380, d = 25, n = ?, Sn = 5000

Therefore I used the formula: n = a + (n-1) x d. But essentially in reverse, I think!

5000 - 380 = 4620 / 25 = 184.5

So if n - 1 = 184.5 then n must equal 185.8 right?

b. What is the total number of toys produced over the first 52 weeks?

Your right this one was more tricky, but i went with this:

Again, variables: a = 380, d = 25, n = 52, Sn = ?

Then the formula; Sn = n/2 (2 x a + (n - 1) x d)

So, 52/2 (2 x 380 + (52 - 1) x 25 = 53,560 = Sn

Some of my peers have made this answer different slightly, but I don't see how?

9 a. If each blow takes 10 seconds how long will it take to drive the post at least 75cm into the ground?

a = 11, r = 0.9, Sn = 75

Sn = a (r^n - 1) / r - 1 (shown as fraction)

75 = 11 (0.9^n - 1) / 0.9 - 1

0.9 - 1 x 75 = -7.5

7.5 = 11 (0.9^n - 1)

Then divide either side by 11

-7.5 / 11 = -0.681 then +1 as both sides have been treated the same = 0.318

0.318 = 0.9^n

Using Logarithm functions:

log 0.9 (0.318) = 10.874 x 10 (seconds) = 108.75 (109)seconds

b. What is the maximum distance the post can be driven into the ground?

Correct me if Im wrong but i believe this answer to technically be infinite, but I still get a figure I can use.

a = 11, r = 0.9

S (infinite symbol) = a / 1 - r

11 / 0.1 = 110cm.

If your not fed up of me by now, I have a few more questions that I need help with!