Question

(a) 2, 3, 6, 11, 18, . . . (i) Write down the next two terms in this sequence. Answer(a)(i) ....................... , ....................... [2] (ii) Describe, in words, the rule for continuing this sequence. Answer(a)(ii) ..........

A tram leaves a station and accelerates for 2 minutes until it reaches a speed of 12 metres per second.
It continues at this speed for 1 minute.
It then decelerates for 3 minutes until it stops at the next station.
The diagram shows the speed-time graph for this journey.
Calculate the distance, in metres, between the two stations.

11 Find the nth term of each sequence.

(b) 11, 20, 35, 56, 83, .......

A car travels a distance of 1280 metres at an average speed of 64 kilometres per hour.
Calculate the time it takes for the car to travel this distance.
Give your answer in seconds.
Answer

Answer 1

(a) Given sequence is

Say are first ,second,.. terms of the sequence .

(1)

That is the sequece 1,3,5,7,9,...(difference of the given sequence ) is airthmatic sequnce with common difference 2 .

hence the next difference is and so on ..

and

that is

(2) The differece of the terms of the given sequence is the airthmatic sequence with common difference 2 .First we find the next two terms (d5,d6) of the difference sequence by using the formula of airthmatic sequence .

Now .