Part 2 - Sequences and Series

Section 2: Sequences and Series

Q11. A sequence is generated by a first-order linear difference equation. The first four terms of this sequence are 1, 3, 7, 15. The next term in the sequence is

A. 17

B. 19

C. 22

D. 23

E. 31

Q12. For an examination, 8600 examination papers are to be printed at a rate of 25 papers per minute. After one hour, the number of examination papers that still need to be printed is

A. 1600

B. 2500

C. 6100

D. 7100

E. 8575

Q13. The values of the first seven terms of a geometric sequence are plotted on the graph below.

Values of a and r that could apply to this sequence are respectively

A. a = 90 r = –0.9

B. a = 100 r = –0.9

C. a = 100 r = –0.8

D. a = 100 r = 0.8

E. a = 90 r = 0.9

Q14. In 2008, there are 800 bats living in a park. After 2008, the number of bats living in the park is expected to increase by 15% per year. Let Bn represent the number of bats living in the park n years after 2008. A difference equation that can be used to determine the number of bats living in the park n years after 2008 is

A.

B.

C.

D.

E.

Q15. The first term of a geometric sequence is 9. The third term of this sequence is 121. The second term of this sequence could be

A. –65

B. –33

C. 56

D. 65

E. 112

Q16. Kai commenced a 12-day program of daily exercise. The time, in minutes, that he spent exercising on each of the first four days of the program is shown in the table below.

If this pattern continues, the total time (in minutes) that Kai will have spent exercising after 12 days is

A. 59

B. 180

C. 354

D. 444

E. 468

Q17. The sequence 12, 15, 27, 42, 69, 111 . . . can best be described as

A. fibonacci-related

B. arithmetic with d > 1

C arithmetic with d < 1

D. geometric with r > 1

E geometric with r < 1

Q18. When placed in a pond, the length of a fish was 14.2 centimetres. During its first month in the pond, the fish increased in length by 3.6 centimetres. During its nth month in the pond, the fish increased in length by Gn centimetres, where Gn+1 = 0.75Gn

The maximum length this fish can grow to (in cm) is closest to

A. 14.4

B. 16.9

C. 19.0

D. 28.6

E. 71.2

Q19. When full, a swimming pool holds 50 000 litres of water. Due to evaporation and spillage the pool loses, on average, 2% of the water it contains each week. To help to make up this loss, 500 litres of water is added to the pool at the end of each week. Assume the pool is full at the start of Week 1. At the start of Week 5 the amount of water (in litres) that the pool contains will be closest to

A. 47 500

B. 47 600

C. 48 000

D. 48 060

E. 48 530

Q20. A pensioner receives a payment of £100 every month for the next 20 years. The pension provider funds for this with a lump sum of money which he places in a bank account receiving 6.5% p.a. interest. How much must he place in the account to ensure that there are sufficient funds to cover the payments?

A. 13400

B. 13500

C. 13600

D. 13700

E. 13800