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In this lesson, we will learn how to solve 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.

Q1:

A man has started working with a yearly salary of 14β700 LE. Find his salary after 6 years if he gets a raise of 600 LE every year.

Q2:

A man has started working with a yearly salary of 20β000 LE. Find his salary after 12 years if he gets a raise of 570 LE every year.

Q3:

The population of a city was 1 3 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 π in millions expressed in terms of the number of years π given the growth is constant and where π = 1 is 2010.

Q4:

The population of a city was 1 2 of a million in 2006 and 8 million in 2016. The population can be described as an arithmetic sequence. Find the linear equation for the population π in millions expressed in terms of the number of years π given the growth is constant and where π = 1 is 2006.

Q5:

The population of a city was 5 7 of a million in 2010 and 5 million in 2016. The population growth can be described as an arithmetic sequence. Find the ratio of population growth given the growth is constant.

Q6:

The population of a city was 1 2 of a million in 2002 and 4 million in 2016. The population growth can be described as an arithmetic sequence. Find the ratio of population growth given the growth is constant.

Q7:

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.

Q8:

A biker rode his motorcycle down a hill and covered a distance of 190 cm in the first second. If the distance covered every second exceeds that of the one before by 290 cm, find the distance covered in the eighteenth second.

Q9:

A man paid for a motorcycle in monthly instalments given by the arithmetic sequence π = 9 5 π + 4 5 π . Find the total number of instalments he must pay given the last instalment to be paid is 2β705 LE.

Q10:

A man paid for a motorcycle in monthly instalments given by the arithmetic sequence π = 9 0 π + 5 0 π . Find the total number of instalments he must pay given the last instalment to be paid is 1β220 LE.

Q11:

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.

Q12:

A doctor prescribed 35 pills for his patient to be taken in the first week. Given that the patient should decrease the dosage by 5 pills every week, find the week in which he will stop taking the medicine completely.

Q13:

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.

Q14:

A man works in a grocery store. He stacks tuna cans in rows, where there are 674 cans in the first row, 667 in the second, 660 in the third, and so on. Find the row which has exactly 625.

Q15:

The population of a city was 8 9 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.

Q16:

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.

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