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Class 9 Maths: Predicting What Comes Next, Sequences and Progressions, 8 practice questions with answers

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These are 8 practice questions on Chapter 8, Predicting What Comes Next: Exploring Sequences and Progressions, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). Each has a worked answer and the textbook page it comes from. They cover the common difference and the nth term of an arithmetic progression (AP), a falling AP, a geometric pattern, the square numbers and the sum of the first n natural numbers. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari: Mathematics, Textbook for Grade 9, Part I, Chapter 8, printed pages 174 to 196):

Arithmetic progressions

Question 1. What is the common difference of the arithmetic progression 7, 11, 15, 19, …?

Answer: 4. Each term is 4 more than the one before: 11 − 7 = 4. (Page 181.)

Question 2. What is the 12th term of 4, 7, 10, 13, ...?

Answer: 37. Each term adds 3, so a = 4 and d = 3. The 12th term = 4 + 11 × 3 = 37. (tn = a + (n − 1) × d, page 181.)

Question 3. In an auditorium, the first row has 28 seats and each row has 3 more seats than the row in front of it. Riya says row 42 has 28 + 42 × 3 = 154 seats. Find her mistake and give the right number.

Answer: 151; she added the difference 42 times instead of 41. Row 1 has 28 seats, and each later row adds 3, so row n has 28 + (n − 1) × 3 seats: row 2 adds one 3, row 3 adds two 3s, and so on. Row 42 adds 41 threes: 28 + 41 × 3 = 28 + 123 = 151 seats. (tn = a + (n − 1) × d, page 181.)

Question 4. In the sequence 100, 93, 86, 79, ..., what is the 8th term?

Answer: 51. Each term takes away 7, so a = 100 and d = −7. The 8th term = 100 − 7 × 7 = 51. (The same formula tn = a + (n − 1) × d works when d is negative, page 181.)

Question 5. Which term of the AP 5, 9, 13, 17, ... is 101? (This question is not in the practice set.)

Answer: the 25th term. Here a = 5 and d = 4, so tn = 5 + (n − 1) × 4. Setting 5 + (n − 1) × 4 = 101 gives (n − 1) × 4 = 96, so n − 1 = 24 and n = 25. Check: 5 + 24 × 4 = 101. (The formula is on page 181; the textbook solves an equation of this kind to ask whether a number is a term of a sequence, page 177.)

Patterns that are not arithmetic progressions

Question 6. What comes next: 2, 6, 18, 54, ...?

Answer: 162. Each term is 3 times the one before (a common ratio of 3), so this is a geometric progression. The next term is 54 × 3 = 162. (Page 187.)

Question 7. What comes next: 1, 4, 9, 16, 25, ...?

Answer: 36. These are the square numbers 1², 2², 3², 4², 5², so the next is 6² = 36. (Pages 174 and 175.)

Sum of natural numbers

Question 8. A shopkeeper stacks 861 tins in rows: 1 tin in the top row, 2 in the next, 3 in the next, and so on, one more in each row. How many rows are there?

Answer: 41 rows. If there are n rows, the number of tins is 1 + 2 + … + n = n(n + 1) ÷ 2. So n(n + 1) ÷ 2 = 861, that is n(n + 1) = 1722. Two consecutive numbers whose product is 1722 lie close to √1722, which is a little over 41: 41 × 42 = 1722. So there are 41 rows. (Sn = n(n + 1) ÷ 2, pages 183 and 184.)

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 173.

The definitions and formulas are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.