5. A path is made from two different types of paving slabs – black (B) slabs and white (W) slabs – as shown. The diagrams show how the path develops after each hour.
W B
B B
W
W W B B
B B
W W
W W W B B B B B
After 1 hour
After 2 hours
(a) Draw the shape of the path after 4 hours. (b) Copy and complete the table below:
After
Number of white tiles Number of black tiles Total number of tiles
(c) Write down a formula for the number Tn of white tiles laid after n hours. (d) Write down a formula for the number Tn of black tiles laid after n hours. (e) Write down a formula for the total number Tn of tiles laid after n hours. (f) How long will it take to lay 296 tiles in total?
6. An athlete’s training programme consists of increasing the distance she runs by 350 m every day. She runs 2 km on the fi rst day.
(a) Write out the distance in metres the athlete runs on the fi rst 4 days of the programme. (b) Explain why the sequence of distances forms an arithmetic sequence. (c) Find the fi rst term and common difference of this arithmetic sequence.
(d) Find the general term Tn of this arithmetic sequence. (e) What distance does the athlete cover on the 10th day of the programme? (f) When will she cover a distance of 4·1 km in one day? (g) Find the total distance she runs in the fi rst 12 days. (h) How many days will it take the athlete to run a total distance of 21·35 km?
