Predicting What Comes Next: Exploring Sequences and Progressions: CBSE Class 9 Mathematics practice questions

Practise 50 questions on Predicting What Comes Next: Exploring Sequences and Progressions, free, with an explanation for each answer.

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Sample questions

These dot triangles show the first four triangular numbers: 1, 3, 6, 10. How many dots are needed for Stage 5?

1. 14
2. 15
3. 16
4. 13

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B. 15

Each triangular number is the sum of the counting numbers up to its stage: $1+2+3+4+5 = 15$. The gaps between terms grow $2, 3, 4, 5, \dots$, so after $10$ we add $5$. Adding $4$ again gives $14$ (forgetting the gap grows), and $16$ is the next square number, not triangular.

For the sequence $t_n = 3n - 7$, which term number is $332$?

1. 111
2. 108
3. 113
4. 339

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C. 113

Set $3n - 7 = 332$, so $3n = 339$ and $n = 113$. So $332$ is the 113th term. Dividing $332$ by $3$ and rounding gives $111$, subtracting $7$ instead of adding gives $108$, and $339$ is the value of $3n$, not the position $n$.

An AP has $50$ terms. Its third term is $12$ and its last term is $106$. What is the 29th term?

1. 64
2. 66
3. 58
4. 62

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A. 64

Subtracting gives $47d = 94$, so $d = 2$ and $a = 12 - 4 = 8$. Then $t_{29} = 8 + 28 \times 2 = 64$. Using $a + 29d = 66$ is the $nd$ slip, $29 \times 2 = 58$ forgets $a$, and $8 + 27 \times 2 = 62$ is one term too early.

Topics covered

• Triangular numbers
• Rules for common sequences
• Notation t_n
• Odd numbers and squares
• Explicit rule
• Position of a term
• Is a number a term?
• Recursive rule
• Recursive rules
• Virahanka-Fibonacci sequence
• Explicit rules
• nth term of an AP
• Graph of an AP
• AP in real life
• Term number of an AP
• Finding a and d
• Sum using S_n
• Sum of natural numbers
• Visual proof of S_n
• Identifying a GP
• AP or not
• Growing GP pattern
• nth term of a GP
• Which term of a GP
• Graph of a GP
• Graphs of AP and GP
• Types of progression
• AP and GP together
• Sierpinski triangle
• Fractals
• Sierpinski carpet
• Bouncing ball GP
• GP in real life
• Counting terms of an AP
• GP from conditions
• Consecutive sums
• Progressions in real life
• Comparing terms

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More CBSE Class 9 Mathematics chapters

• Orienting Yourself: The Use of Coordinates
• Introduction to Linear Polynomials
• The World of Numbers
• Exploring Algebraic Identities
• I’m Up and Down, and Round and Round
• Measuring Space: Perimeter and Area
• The Mathematics of Maybe: Introduction to Probability
• Propositions and Their Converses
• How Quantities Combine: Understanding Data
• The World of Algorithms
• Quadrilaterals
• Two Variables, One Line
• Math of Space: Surface Area and Volume