Question 1
Paper 2, calculatorMedium6 marksA small venue records its ticket sales over five weeks.
| Week | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Tickets sold | 420 | 458 | 491 | 530 | 563 |
The sales do not form an exact arithmetic sequence. An arithmetic model is used, with its first and fifth terms matching the recorded sales for weeks 1 and 5.
(a)[1]
Determine the common difference of this model.
(b)[2]
Hence estimate the number of tickets sold in week 9.
(c)[2]
State the first term and common difference of your model. Write the model’s total predicted ticket sales for weeks 1 to 9 in sigma notation, and determine this total. You may use your GDC.
(d)[1]
Give one reason why the model’s estimate for week 9 may differ from the actual number of tickets sold.