0 votes, 0 avg

SCROLL DOWN

QM [ Mathematical progression ]

Understanding Mathematical Progressions

Mathematical progressions are fundamental concepts in mathematics that involve sequences of numbers arranged in a specific order. The two most common types of mathematical progressions are arithmetic progressions (AP) and geometric progressions (GP). Understanding these progressions is essential for various applications in finance, science, and engineering. This article delves into the definitions, properties, and applications of both types of progressions.

Arithmetic Progression (AP)

Definition

An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. This difference is known as the common difference. For example, in the sequence 2, 5, 8, 11, the common difference is 3.

Key Characteristics

Constant Difference: The difference between any two successive terms remains the same throughout the sequence.
Linear Growth: The n-th term can be expressed as a linear function of n, which means it grows steadily.
Sum of Terms: The sum of the first n terms can be calculated easily using a specific method, which helps in determining total savings, payments, or any cumulative value over time.

Example

Consider a scenario where a person saves a certain amount of money each month. If the first month’s savings is Rs. 500 and he continues to save Rs. 300 more each subsequent month, the amount saved forms an arithmetic progression.

Geometric Progression (GP)

Definition

A geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number known as the common ratio. For example, in the sequence 3, 6, 12, 24, the common ratio is 2.

Key Characteristics

Constant Ratio: The ratio between any two successive terms is constant, which leads to exponential growth.
Exponential Growth: The n-th term grows rapidly, making geometric progressions useful in scenarios involving growth over time.
Sum of Terms: The sum of the first n terms can also be calculated through a specific method, which is especially useful in financial contexts, such as calculating compound interest.

Example

Consider an investment scenario where a person invests Rs. 1,000 in a fund that doubles its value each year. The returns on the investment form a geometric progression, demonstrating rapid growth.

Applications of Mathematical Progressions

Mathematical progressions have a wide range of applications in various fields:

Finance: In finance, arithmetic progressions are used to calculate loan repayments, while geometric progressions help in calculating compound interest and growth of investments over time. Understanding these progressions enables individuals and businesses to make informed financial decisions.
Computer Science: Algorithms often rely on sequences for searching and sorting processes, where understanding the nature of growth (arithmetic or geometric) can help optimize performance. Knowing how data grows can lead to more efficient coding practices.
Physics: Many physical phenomena can be modeled using progressions, such as the decay of radioactive materials (geometric progression) or the motion of an object under constant acceleration (arithmetic progression). These models help in predicting future behavior of systems.
Statistics: In statistics, arithmetic and geometric means are important concepts derived from these progressions, which are used in various data analysis techniques. Understanding how to apply these means is crucial in interpreting data accurately.

Conclusion

Understanding mathematical progressions is crucial for students and professionals alike. Mastery of arithmetic and geometric progressions provides valuable tools for solving real-world problems, especially in fields such as finance, science, and engineering. By familiarizing oneself with these concepts, one can apply them effectively in various applications.

Mathematical progressions are not just abstract concepts; they are practical tools that aid in decision-making and forecasting in many aspects of life. Grasping these ideas can significantly enhance analytical skills and provide a solid foundation for more advanced mathematical studies.

1 / 23

1. If Ahmad saves Rs. 1,000 in the first month and 500 more every month, how much time he
needs to save Rs. 45,000

a) 9

b) 12

c) 8

d) 16

2 / 23

2. If someone invest Rs 6,000 as 1st instalment and increase by Rs.300 per month in each of
next instalment for 24 months which of the following is true
1. Rs. 119,900 is the total value received after 13th instalment
2. The value for 13th instalment is Rs. 9,900

a) Only i is correct.

b) Only ii is correct.

c) Both are correct.

d) none

3 / 23

3. Mr. Ali has borrowed X amount of money. He agreed to pay the installment 1.2 times than
the last one. If his fifth installment is Rs. 51,389, what was his first installment?

a) 51,384.2

b) 24,782.5

c) 20,652.1

d) Cannot be calculated

4 / 23

4. If a person invests 2 million and withdraw 10% each month then how much time it will take
to end of investment?

a) 5 months

b) 15 months

c) 10 months

d) 20 months

5 / 23

5. XYZ and Company has developed a new product that would earn a revenue of Rs. 80 million during the first year. The revenue is expected to decline by 20% each subsequent year. What will be the total revenue earned by the company over the life of the product?

a) Rs. 240 million

b) Rs. 256 million

c) Rs. 320 million

d) Rs. 300 million

6 / 23

6. Mr. Adeel saved Rs x in January, then each subsequent month he saved Rs 100 more than the
previous month. If his total savings at the end of December stood at Rs 16,200 how much did
he save in January?

a) 700

b) 800

c) 900

d) 1000

7 / 23

7. Which of the following equations represents a line that is parallel to the x-axis?

a) y=2

b) x=3

c) 3y−6=0

d) y=−x+5

8 / 23

8. ABC and Company has developed a new product which would earn a revenue of Rs 80
million during the first year. Thereafter, the revenue would decline by 20% each year.
Calculate the revenue that the company would be able to earn over the life of the product

a) 400 million

b) 500 million

c) 800 million

d) 100 million

9 / 23

9. XYZ and Company has developed a new product which would earn a revenue of Rs 90
million during the first year. Thereafter, the revenue would decline by 10% each year.
Calculate the revenue that the company would be able to earn over the life of the product

a) 450 million

b) 500 million

c) 900 million

d) 1 billion

10 / 23

10. Ali borrowed Rs. 1,500,000 on first year he returned Rs. 80,000 and then he increases his
instalment by 1.5 times of the previous instalment every year. In how many years he will be
able to return the loan?

a) 6 years

b) 8 years

c) 12 years

d) 16 years

11 / 23

11. Ali borrowed Rs. 1,500,000 on first year he returned Rs. 80,000 and then he increases his
instalment by 1.2 times of the previous instalment every year. In which years he will be able
to return the loan?

a) 9 years

b) 6 years

c) 8 years

d) 10 years

12 / 23

12. Which of the following pairs of values cannot form part of a Geometric Progression?

a) √5 and √7

b) 1,000,000 and 0

c) (6 and -6)

d) All of the above

13 / 23

13. Ali receives a total of Rs. 288,000 in two years in the form of monthly installments. If he
receives 1000 more than the previous month calculate the first installment?

a) Rs 7,500

b) Rs 6,500

c) Rs 500

d) None of these

14 / 23

14. Ali has to pay Rs. 1,600,000 in installments. He pays the first installment of Rs. 60,000 and increases each subsequent installment by a factor of 1.9. In which year will he complete the payment?

a) Year 20

b) Year 25

c) Year 30

d) Year 35

15 / 23

15. If Matti save Rs. 426000 monthly in two years. If he saves 500 in first month by x. Find the
amount of last installment

a) 40000

b) 35000

c) 36000

d) 33000

16 / 23

16. In an arithmetic progression, the sum of the first terms is equal to $5n+3n^2$ What is the common difference?

a) 6

b) 5

c) 3

d) 7

17 / 23

17. If the 4th term of a geometric progression is 64 and the 2nd term is 16, what is the first term?

a) 8

b) 4

c) 2

d) 1

18 / 23

18. A person invests Rs. 5,000 in an account that pays an interest of 5% per month. If he adds Rs. 500 at the end of each month, how much will he have in the account after 6 months?

a) 6,500

b) 7,500

c) 8,000

d) 8,500

19 / 23

19. In a geometric progression, if the first term is 3 and the sum of the first three terms is equal to 39, what is the common ratio?

a) 2

b) 3

c) 4

d) 5

20 / 23

20. In an arithmetic progression, the sum of the first terms is equal to n^2+5n. If the product of the first four terms is equal to 57,600, find the value of $n$ .

a) 8

b) 10

c) 12

d) 14

21 / 23

21. If the slope of a line is 0, which of the following statements is true?

a) The line is vertical.

b) The line is horizontal.

c) The line intersects the y-axis at 0.

d) The line has no slope.

22 / 23

22. The first term of an arithmetic progression is and the common difference is . What is the sum of the first 15 terms?

a) 750

b) 780

c) 800

d) 825

23 / 23

23. If the first term of an arithmetic sequence is $a$ and the sum of the first 10 terms is 500, while the sum of the first 20 terms is 1,500, what is the value of $a$ ?

a) 10

b) 15

c) 20

d) 25

Your score is

The average score is 37%

Ch 3 Mathematical progression.

Understanding Mathematical Progressions

Arithmetic Progression (AP)

Definition

Key Characteristics

Example

Geometric Progression (GP)

Definition

Key Characteristics

Example

Applications of Mathematical Progressions

Conclusion

Leave a ReplyCancel Reply

Understanding Mathematical Progressions

Arithmetic Progression (AP)

Definition

Key Characteristics

Example

Geometric Progression (GP)

Definition

Key Characteristics

Example

Applications of Mathematical Progressions

Conclusion

Leave a ReplyCancel Reply

Trending now