1. 1
   A theatre has 25 rows of seats. The first row has 18 seats and each row after the first has 3 more seats than the row in front of it.

   (a)

   Find the number of seats in the 25th row.

   [1 mark]

   • A90
   • B93
   • C75
   • D87

   (b)

   Find the total number of seats in the theatre.

   [1 mark]

   • A2700
   • B1350
   • C2250
   • D1387.5

   (c)

   Find the number of the first row that has more than 60 seats.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Consider the series $\displaystyle\sum_{r=1}^{n}(7r-2)$.

   (a)

   Write down the first term and the common difference of the series.

   [1 mark]

   • A$u_1 = -2,\ d = 7$
   • B$u_1 = 7,\ d = -2$
   • C$u_1 = 5,\ d = 7$
   • D$u_1 = 5,\ d = 5$

   (b)

   Find the value of the series when $n = 20$.

   [1 mark]

   • A2860
   • B1470
   • C1468
   • D1430

   (c)

   Given that $\displaystyle\sum_{r=1}^{n}(7r-2) = 3195$, find the value of $n$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Leila invests 4000 AED in an account that pays simple interest at 3.5% per year. Her brother Omar invests 5000 AED at the same time in an account that pays simple interest at 2.2% per year. Neither of them makes any further deposits or withdrawals.

   (a)

   Show that the value of Leila's investment at the end of year $n$ is $4000 + 140n$ AED, and explain why the values at the end of each year form an arithmetic sequence.

   [3 marks]

   (b)

   Find the number of complete years after which the value of Leila's investment first exceeds the value of Omar's investment.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A runner records her total training distance each week. In weeks 1 to 5 she runs 12.0 km, 14.6 km, 17.1 km, 19.8 km and 22.5 km. Her coach wants to model the weekly distance with an arithmetic sequence whose first term is 12.0 km.

   (a)

   (i) Find the differences between consecutive weekly distances and explain why the data are not exactly arithmetic.
   (ii) Using the mean of these differences as the common difference, write down an expression for $u_n$, the model's weekly distance in week $n$.
   (iii) Use the model to predict the distance run in week 12, and comment on the reliability of this prediction.

   [6 marks]

   (b)

   The runner follows the model each week until the model's distance would exceed 42.2 km. From that week onwards she runs exactly 42.2 km each week.
   (i) Find the total distance the model predicts for the first 16 weeks.
   (ii) Find the first week in which the model's distance exceeds 42.2 km.
   (iii) Hence find the total distance she actually plans to run in the first 16 weeks.

   [6 marks]

   Total for question 4: 12 marks

End of questions