# 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.

**Q3: **

The population of a city was 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 in millions expressed in terms of the number of years given the growth is constant and where is 2010.

- A
- B
- C
- D

**Q4: **

The population of a city was 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.

- A5
- B
- C
- D
- E

**Q5: **

A man paid for a motorcycle in monthly instalments given by the arithmetic sequence . Find the total number of instalments he must pay given the last instalment to be paid is 2β705 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 seventh week
- Din the sixth week
- Ein the eighth 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 seventh row
- Bthe fifth row
- Cthe fourth row
- Dthe sixth row
- Ethe sixteenth row

**Q8: **

The population of a city was 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: **

Adelβs annual salary increases by the same quantity every year. In her year at her job, she earned . In her 10th year, she earned . How much will she earn in her year?

**Q11: **

Maged and Farida are trying to work out the sum of the arithmetic series . They graphed the sequence , 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 .

- A
- B
- C
- D
- E

Farida was very excited about their findings and said, βSo 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!β Maged objected that it would work only for an even number of terms. Farida then drew this graph.

The calculation allows us to work out the area of the rectangle shown in the diagram. Farida actually wants to calculate the sum of the series . What is this sum in terms of the area of the rectangle?

- Ahalf the area of the rectangle
- Bthe area of the rectangle
- Cdouble the 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 sum of the first and last terms of the sequence
- B the number of terms of the sequence

**Q12: **

Find the fourth term in the sequence of natural numbers, which is exactly 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
- B
- C
- D

**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 .

- A
- B
- C
- D

**Q16: **

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