A woman saves $50 of her salary in a certain month and in each successive month she saves $4 more than the previous month. How much does she save in two years?

Given that \(\dfrac{1}{a},\,\dfrac{1}{x},\,\dfrac{1}{b}\) are in arithmetic sequence

(i)  Show that \(x = \dfrac{{2ab}}{{a + b}}\)

(ii)  Hence show that \({x^2} = (x - 2a)(x - 2b)\)

A plant is 100 cm high when first measured. In the first month of observation it grows 20 cm and in each succeeding month the growth is 50% of the previous week's growth. If this pattern continues, what will be the plant's ultimate height?

If \(8,x,y\) form a geometric sequence and \(x,y,24\) form an arithmetic sequence, then the values of \(x\) and \(y\) are?  

A truck travels 100 km to load 1 ton of coal and then returns to its base. It then travels 120 km, loads another 1 ton of coal further away from the first and returns to base.

If the distances that the truck travels each time form an arithmetic sequence then

i) show that the total distance travelled, for \(n\) trips, is \(20n(n+9)\) km.

ii) If the price for coal is $600 per trip and the travelling costs are $2 per km, calculate the number of trips possible before the total distance travelled makes the collection unprofitable.

iii) Using your calculator, determine the number of trips that will yield a maximum profit.

A golf ball is dropped from a height of 12 m onto a stone pavement. After each bounce, the maximum height reached by the ball is one third of the previous maximum height.

i) What height does it reach on its second bounce?

ii) How far has it travelled when it strikes the pavement on the fourth occasion?

The numbers \(y - 1, y - 10, y + 8\) form a geometric sequence, determine the next term in the sequence

\(x,y,x + y\) form an A.P. and \(x,y,20\) form a G.P. Find the values of \(x\) and \(y\)

If \(4,x,y\) form a G.P. and \(x,y,12\) form an A.P. then the values of \(x\) and \(y\) are?

The 6th term of log 6, log 12, log 24, ... is?

How many multiples of 9 are between 200 and 400?

Find the values of \(x\) for which the terms \(x - 1, x + 5, 5x + 3,\) form an A.P.

Find the value of \(y\) for which the terms \(y - 1, y - 10, y + 8\) form a G.P.

A truck travels 100km to load 1 ton of coal and then returns to its base. It then travels 120km, loads another 1 ton of coal further away from the first and returns to base. 

If the distances that the truck travels each time from an arithmetic sequence then

i) Show that the total distance travelled, for \(n\) tripe, is \(20n(n+9)\,km\)

ii) If the price of coal is \(\$600\) per ton and the travelling costs are \(\$2\) per km, calculate the number of trips possible before the total distance travelled makes the collection unprofitable. 

iii) Determine the number of trips that will yeild a maximum profit