# NCERT Class 8 Mathematics Chapter 12 Tales by Dots and Lines Solutions: In-Text and Exercise Questions Explained | SwaVid

This document provides real questions from the NCERT Class 8 Mathematics textbook "Ganita Prakash-II", specifically from Chapter 5, titled "Tales by Dot...

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# Tales by Dots and Lines

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Chapter 12 · Class 8 Mathematics

This document provides real questions from the NCERT Class 8 Mathematics textbook "Ganita Prakash-II", specifically from Chapter 5, titled "Tales by Dots and Lines". The questions include both in-text 'Figure It Out' problems and their step-by-step solutions, designed to be followed by a Class 8 student.

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Figure It Out (Pages 113-116)

Answer: (i) Mean = 25.5. Observation: Mean of first n natural numbers is (n+1)/2. (ii) Mean = 50. Observation: Mean of first n odd numbers is n. (iii) Mean = 102. Observation: Mean of first n multiples of 4 is 4 times the mean of first n natural numbers.

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- **(i) The first 50 natural numbers:**
- The first 50 natural numbers are 1, 2, 3, ..., 50.
- The sum of the first 'n' natural numbers is given by the formula S = n(n+1)/2. For n = 50, the sum is S = 50(50+1)/2 = 50 * 51 / 2 = 25 * 51 = 1275.
- The mean is the sum divided by the number of values: Mean = 1275 / 50 = 25.5.
- Observation: The mean of the first 'n' natural numbers is always (n+1)/2. For n=50, the mean is (50+1)/2 = 51/2 = 25.5.
- **(ii) The first 50-odd numbers:**
- The first 50-odd numbers are 1, 3, 5, ..., 99.
- The sum of the first 'n' odd numbers is given by the formula S = n². For n = 50, the sum is S = 50² = 2500.
- The mean is the sum divided by the number of values: Mean = 2500 / 50 = 50.
- Observation: The mean of the first 'n' odd numbers is always 'n'. For 50 odd numbers, the mean is 50.
- **(iii) The first 50 multiples of 4:**
- The first 50 multiples of 4 are 4, 8, 12, ..., 200.
- This is equivalent to 4 times the first 50 natural numbers: 4 * (1, 2, 3, ..., 50).
- The sum of these numbers is 4 times the sum of the first 50 natural numbers: 4 * 1275 = 5100.
- The mean is the sum divided by the number of values: Mean = 5100 / 50 = 102.
- Observation: The mean of the first 'n' multiples of 4 is 4 times the mean of the first 'n' natural numbers. So, 4 * 25.5 = 102.
- NCERT Class 8 Mathematics textbook: Ganita Prakash-II : Chapter 12: Tales by Dots and Lines

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