# NCERT Class 9 Mathematics Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions Solutions: In-Text and Exercise Questions Explained | SwaVid

This chapter, 'Predicting What Comes Next: Exploring Sequences and Progressions' from the NCERT Class 9 Mathematics textbook 'Ganita Manjari', introduce...

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# Predicting What Comes Next: Exploring Sequences and Progressions

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Chapter 8 · Class 9 Mathematics

This chapter, 'Predicting What Comes Next: Exploring Sequences and Progressions' from the NCERT Class 9 Mathematics textbook 'Ganita Manjari', introduces students to various types of number sequences and progressions. It covers concepts such as identifying patterns, explicit and recursive rules for sequences, arithmetic progressions (AP), and geometric progressions (GP). The exercises aim to develop skills in finding terms of a sequence, determining if a number belongs to a sequence, and solving real-world problems involving progressions.

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In-text Questions and Exercises

Answer: (i) Natural Numbers: Pattern: Add 1 to the previous term. Next terms: 7, 8, 9, 10, 11. (ii) Odd Numbers: Pattern: Add 2 to the previous term. Next terms: 13, 15, 17, 19, 21. (iii) Triangular Numbers: Pattern: Sum of natural numbers up to the term's position. Next terms: 28, 36, 45, 55, 66. (iv) Square Numbers: Pattern: Square of the term's position. Next terms: 49, 64, 81, 100, 121.

Exercise Set 8.1

Exercise Set 8.2

Exercise Set 8.3

End-of-Chapter Exercises

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- For Natural Numbers (1, 2, 3, 4, 5, 6, …): The pattern is that each term is obtained by adding 1 to the previous term. The next few numbers would be 7, 8, 9, 10, 11, ….
- For Odd Numbers (1, 3, 5, 7, 9, 11, ...): The pattern is that each term is obtained by adding 2 to the previous term. The next few numbers would be 13, 15, 17, 19, 21, ….
- For Triangular Numbers (1, 3, 6, 10, 15, 21, ...): The pattern is that each term is the sum of natural numbers up to its position. For example, the 1st term is 1, the 2nd term is 1+2=3, the 3rd term is 1+2+3=6, and so on. The next few numbers would be 28 (21+7), 36 (28+8), 45 (36+9), 55 (45+10), 66 (55+11), ….
- For Square Numbers (1, 4, 9, 16, 25, 36, ...): The pattern is that each term is the square of a natural number. For example, the 1st term is 1²=1, the 2nd term is 2²=4, the 3rd term is 3²=9, and so on. The next few numbers would be 49 (7²), 64 (8²), 81 (9²), 100 (10²), 121 (11²), ….
- NCERT Class 9 Mathematics textbook: Ganita Manjari : Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions

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