Real-world AP: find term or total

Model a practical scenario (salary, savings, charity donations, training runs) as an arithmetic sequence and find a specific term value or total amount after n periods.

29 questions · Moderate -0.8

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Edexcel M2 2014 January Q7
10 marks Easy -1.2
Shelim starts his new job on a salary of £14000. He will receive a rise of £1500 a year for each full year that he works, so that he will have a salary of £15500 in year 2, a salary of £17000 in year 3 and so on. When Shelim's salary reaches £26000, he will receive no more rises. His salary will remain at £26000.
  1. Show that Shelim will have a salary of £26000 in year 9. [2]
  2. Find the total amount that Shelim will earn in his job in the first 9 years. [2]
Anna starts her new job at the same time as Shelim on a salary of £\(A\). She receives a rise of £1000 a year for each full year that she works, so that she has a salary of £\((A + 1000)\) in year 2, £\((A + 2000)\) in year 3 and so on. The maximum salary for her job, which is reached in year 10, is also £26000.
  1. Find the difference in the total amount earned by Shelim and Anna in the first 10 years. [6]
Edexcel C1 Q4
8 marks Moderate -0.8
In the first month after opening, a mobile phone shop sold 280 phones. A model for future trading assumes that sales will increase by \(x\) phones per month for the next 35 months, so that \((280 + x)\) phones will be sold in the second month, \((280 + 2x)\) in the third month, and so on. Using this model with \(x = 5\), calculate
    1. the number of phones sold in the 36th month, [2]
    2. the total number of phones sold over the 36 months. [2]
The shop sets a sales target of 17000 phones to be sold over the 36 months. Using the same model,
  1. find the least value of \(x\) required to achieve this target. [4]
Edexcel C1 Q9
10 marks Moderate -0.8
A store begins to stock a new range of DVD players and achieves sales of £1500 of these products during the first month. In a model it is assumed that sales will decrease by £\(x\) in each subsequent month, so that sales of £\((1500 - x)\) and £\((1500 - 2x)\) will be achieved in the second and third months respectively. Given that sales total £8100 during the first six months, use the model to
  1. find the value of \(x\), [4]
  2. find the expected value of sales in the eighth month, [2]
  3. show that the expected total of sales in pounds during the first \(n\) months is given by \(kn(51 - n)\), where \(k\) is an integer to be found. [3]
  4. Explain why this model cannot be valid over a long period of time. [1]
SPS SPS SM 2022 October Q3
7 marks Moderate -0.8
A 25-year programme for building new houses began in Core Town in the year 1986 and finished in the year 2010. The number of houses built each year form an arithmetic sequence. Given that 238 houses were built in the year 2000 and 108 were built in the year 2010, find
  1. the number of houses built in 1986, the first year of the building programme, [5]
  2. the total number of houses built in the 25 years of the programme. [2]