Case Study Class 10 Arithmetic Progression

Case Study Class 10 Arithmetic Progression Overview

Understanding Case Study Class 10 is crucial for exams. Students often practice with math case study questions class 10 to build confidence. These problems involve sequences where each term follows a rule. Additionally, solving Case Study math questions for class 10 and math case study questions class 10 prepares students for higher-level concepts. Therefore, focusing on this topic strengthens both analytical and problem-solving skills effectively.

Case Study Questions Arithmetic Progression Class 10

In Case Study Class 10 , questions often highlight real-life situations. For example, calculating savings, distances, or patterns in daily life. Practicing math case study questions helps students connect classroom learning with practical use. Moreover, working on Case Study Questions Class 10 ensures better exam preparation. As a result, students gain confidence, accuracy, and speed. Importantly, these case studies encourage logical thinking along with systematic application of formulas.

Case Study 1

Rohit is fond of reading novels and sets a personal target for himself. On the first day, he reads 12 pages, on the second day 17 pages, on the third day 22 pages, and continues this pattern of reading. His aim is to complete a novel of 600 pages. The number of pages he reads each day forms an arithmetic progression (AP). Using the concepts of Arithmetic Progressions, let us analyze his reading pattern and answer the following questions.

The general form of an Arithmetic Progression is:

\[a, a+d, a+2d, a+3d, \ldots\]

where \(a\) is the first term and \(d\) is the common difference.

The \(n\)th term is given by:

\[a_n = a + (n-1)d\]

The sum of the first \(n\) terms is given by:

\[S_n = \frac{n}{2} \big(2a + (n-1)d\big)\]

1. What is the common difference \(d\) of the AP formed by Rohit’s reading pattern?

  • A) 4
  • B) 5
  • C) 6
  • D) 7
Answer: B) 5
Solution: The first three terms are 12, 17, 22. \(d = 17 – 12 = 5\).

2. What will be the number of pages Rohit reads on the 10th day?

  • A) 52
  • B) 57
  • C) 60
  • D) 62
Answer: B) 57
Solution: \(a = 12\), \(d = 5\), \(n=10\). \(a_{10} = a + (n-1)d = 12 + 9(5) = 57\).

3. How many pages will Rohit read in the first 20 days?

  • A) 1200
  • B) 1300
  • C) 1400
  • D) 1500
Answer: 1190 pages (Note: None of the options match the correct calculation)
Solution: \(a=12\), \(d=5\), \(n=20\). \(S_{20} = \dfrac{20}{2} [2(12) + (20-1)(5)] = 10(24 + 95) = 10(119) = 1190\).

4. On which day will Rohit read exactly 87 pages?

  • A) 14th day
  • B) 15th day
  • C) 16th day
  • D) 17th day
Answer: C) 16th day
Solution: \(a_n = 12 + (n-1)(5) = 87\). \((n-1)(5) = 75 \implies n-1 = 15 \implies n=16\).

5. After how many days will Rohit complete reading the 600 pages novel?

  • A) 20 days
  • B) 22 days
  • C) 23 days
  • D) 24 days
Answer: C) 23 days
Solution: We need \(S_n = 600\). \(S_n = \dfrac{n}{2} [2(12) + (n-1)(5)] = 600\). Solving the equation \(5n^2 + 19n – 1200 = 0\), we get \(n=23\).

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