1) Water fills a tank at a rate of 150 litres during the first hour, 350 litres during the second, 550 during the third and so on. Find the number of hours necessary to fill a rectangular tank 16m x 9m x 9m.
2) A firm starts work with 110 employees for the 1st week. the number of the employees rises by 6% for the first week. how many persons will be employed in the 20th week if the present rate of expansion continues.
3) a contractor hires out machinery. in the first year of hiring out one piece of equipment the profit is $6000, but this diminishes by 5% in successive years. show that the annual profits form a geometric progression and find the total of all the profits for the first 5 years.
1) Total volume = 16x9x9 = 1296 cubic metres = 1296000 litres
Common Difference =
Sum to n-terms:
As n must be positive, n=113.59 or 114 (if rounding up)
For 2, use the same process as above, simply replacing the common difference, d, with the common ratio, r such that and repeat, and in 3 rearrange the equation for to obtain n, and solve.