Worksheet: Applications of Arithmetic Sequences

In this worksheet, we will practice solving real-world applications of arithmetic sequences where we will find the common difference, nth term explicit formula and order and value of a specific sequence term through real-world context.

Q1:

A biker rode his motorcycle down a hill and covered a distance of 100 cm in the first second. If the distance covered every second exceeds that of the one before by 120 cm, find the distance covered in the thirteenth second.

Q2:

A man has started working with a yearly salary of 14,700 LE. Find his salary after 6 years if he gets a raise of 600 LE every year.

Q3:

The population of a city was 13 of a million in 2010 and 5 million in 2016. The population can be described as an arithmetic sequence. Find the linear equation for the population 𝑝 in millions expressed in terms of the number of years 𝑛 given the growth is constant and where 𝑛=1 is 2010.

  • A 𝑝 = 1 9 ( 7 𝑛 + 1 0 )
  • B 𝑝 = 1 9 ( 7 𝑛 βˆ’ 4 )
  • C 𝑝 = 1 2 1 ( 2 7 𝑛 βˆ’ 2 0 )
  • D 𝑝 = 1 2 1 ( 2 7 𝑛 + 3 4 )

Q4:

The population of a city was 57 of a million in 2010 and 5 million in 2016. The population growth can be described as an arithmetic sequence. Find its constant difference, which represents the annual growth of the population.

  • A 1 7
  • B 7 5
  • C5
  • D 5 8
  • E 5 7

Q5:

A man paid for a motorcycle in monthly instalments given by the arithmetic sequence π‘Ž=95𝑛+45. Find the total number of instalments he must pay given the last instalment to be paid is 2,705 LE.

Q6:

A doctor prescribed 15 pills for his patient to be taken in the first week. Given that the patient should decrease the dosage by 3 pills every week, find the week in which he will stop taking the medicine completely.

  • Ain the fourth week
  • Bin the fifth week
  • Cin the sixth week
  • Din the eighth week
  • Ein the seventh week

Q7:

A man works in a grocery store. He stacks tuna cans in rows, where there are 39 cans in the first row, 37 in the second, 35 in the third, and so on. Find the row which has exactly 29.

  • Athe sixth row
  • Bthe seventh row
  • Cthe fifth row
  • Dthe fourth row
  • Ethe sixteenth row

Q8:

The population of a city was 89 of a million in 1999 and 16 million in 2016. If it can be described as an arithmetic sequence, find the population in 2019 to the nearest million given the population growth is constant.

Q9:

A man works in a grocery store. He stacks tuna cans in rows, where there are 92 cans in the first row, 89 in the second, 86 in the third, and so on. Find the number of cans in the twelfth row.

Q10:

Emma’s annual salary increases by the same quantity every year. In her 4th year at her job, she earned $24,000. In her 10th year, she earned $36,000. How much will she earn in her 20th year?

Q11:

Benjamin and Scarlett are trying to work out the sum of the arithmetic series 1+3+5+7+9+11. They graphed the sequence 1,3,5,7,9, and 11 as shown in the diagram.

They realized that they can actually rearrange the graph in this way. Write the calculation that gives the sum of the series 1+3+5+7+9+11.

  • A 1 2 Γ— 2
  • B 1 2 Γ— 3
  • C 1 1 Γ— 4
  • D 1 2 Γ— 4
  • E 1 1 Γ— 3

Scarlett was very excited about their findings and said, β€œSo to find the sum of all the terms of an arithmetic sequence, we just need to add the first and last terms and multiply the result by half the number of terms!” Benjamin objected that it would work only for an even number of terms. Scarlett then drew this graph.

The calculation 7Γ—14 allows us to work out the area of the rectangle shown in the diagram. Scarlett actually wants to calculate the sum of the series 1+3+5+7+9+11+13. What is this sum in terms of the area of the rectangle?

  • Adouble the area of the rectangle
  • Bhalf the area of the rectangle
  • Cthe area of the rectangle

What does the 14 in the calculation of the area stand for, with respect to the series?

  • Athe number of terms of the sequence
  • Bthe sum of the first and last terms of the sequence

What does the 7 in the calculation of the area stand for, with respect to the series?

  • Athe number of terms of the sequence
  • Bthe sum of the first and last terms of the sequence

Q12:

Find the fourth term in the sequence of nonnegative integers that are divisible by 99.

Q13:

Find the first six terms of the sequence of numbers between 64 and 92 which are exactly divisible by 4.

  • A ( 6 8 , 7 2 , 7 6 , 8 0 , 8 4 , 8 8 )
  • B ( 6 4 , 6 8 , 7 2 , 7 6 , 8 0 , 8 4 )
  • C ( 6 8 , 7 6 , 8 0 , 8 4 , 8 8 , 9 2 )
  • D ( 7 2 , 7 6 , 8 0 , 8 4 , 8 8 , 9 2 )

Q14:

The annual cost of science club membership is 95 LE. The cost increases by 20 LE every year. How much will it cost in 9 years?

Q15:

Write the first six terms of the sequence of negative odd numbers starting from βˆ’1.

  • A βˆ’ 1 , βˆ’ 2 , βˆ’ 5 , βˆ’ 7 , βˆ’ 9 , βˆ’ 1 1
  • B βˆ’ 1 , βˆ’ 2 , βˆ’ 3 , βˆ’ 4 , βˆ’ 5 , βˆ’ 6
  • C βˆ’ 1 , βˆ’ 5 , βˆ’ 7 , βˆ’ 9 , βˆ’ 1 1 , βˆ’ 1 3
  • D βˆ’ 1 , βˆ’ 3 , βˆ’ 5 , βˆ’ 7 , βˆ’ 9 , βˆ’ 1 1

Q16:

Mason’s exercise plan lasts for 6 minutes on the first day and increases by four minutes each day. For how long will Mason exercise on the eighteenth day?

Q17:

A 10-year housing development project consists of constructing new houses in an unused area of Bristol. 290 houses are built in the third year and 395 in the sixth year. If the number of houses built each year forms an arithmetic sequence, how many houses will be built in total over the 10 years?

Q18:

David has a physics exam where he earns 4 points for each question that he answers correctly. In the table, 𝑛 represents the number of questions that he answers correctly, and 𝑑 represents the total number of points that he scores. Suppose he scored a total of 60 points on his physics exam. How many questions did he answer correctly?

𝑛 1 2 3 4
𝑑 4 8 12 16

Q19:

On the first day, a person exercised for 26 minutes. After that, he increased the time they exercised by two minutes each day. On which day did they exercise for half an hour?

  • AOn the Twentieth day
  • BOn the Third day
  • COn the Seventh day
  • DOn the Fourteenth day

Q20:

The cost of storing a 1 m3 box for one day is Β£5.49, whereas, the cost of storage for two days is Β£6.23. Given that the cost of storage can be described as an arithmetic sequence, how much would it cost to store 8 boxes for 15 days?

Q21:

Victoria is training for a 10 km race. On each training day, she runs 0.5 km more than the previous day. If she completes 4 km on her fourth day, on what day will she complete 10 km?

Q22:

Emma is conducting a series of science experiments that involve using increasing amounts of acetic acid. She used 8.2 mL of acetic acid in the first experiment and 11.0 mL in the fifth experiment. Given the increase in acetic acid can be described using an arithmetic sequence, how much acetic acid will she use in the 18th experiment?

Q23:

The side lengths of a 5-sided polygon form an arithmetic sequence. If the length of the shortest side is 7 meters, and the length of the next longest side is 10 meters, what is the length of the longest side?

Q24:

A cable television offers its service at $45 per month and a one-time setup fee of $19.95. Express the total amount paid 𝑃(𝑛) after 𝑛β‰₯0 months by a recursive formula.

  • A 𝑃 ( 𝑛 + 1 ) = 𝑃 ( 𝑛 ) + 4 5 , 𝑃 ( 0 ) = 1 9 . 9 5
  • B 𝑃 ( 𝑛 + 1 ) = 𝑃 ( 𝑛 ) + 4 5 𝑛
  • C 𝑃 ( 𝑛 ) = 1 9 . 9 5 + 4 5 𝑛
  • D 𝑃 ( 𝑛 + 1 ) = 1 9 . 9 5 + 4 5 𝑛
  • E 𝑃 ( 𝑛 ) = 𝑃 ( 𝑛 βˆ’ 1 ) + 4 5 , 𝑃 ( 0 ) = 4 5

Q25:

Isabella started working out to get healthier. She worked out for fourteen minutes on the first day and increased her exercise by six minutes every day. Find, in terms of 𝑛, the 𝑛th term of the sequence which represents her plan.

  • A 6 𝑛 + 9
  • B 1 4 𝑛 + 1 2
  • C 6 𝑛 + 1 4
  • D 8 𝑛 + 6

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