Are the practice questions for Predicting What Comes Next: Exploring Sequences and Progressions free?

Yes. Every chapter includes free practice questions for Class 9 students to get you started.

What types of questions are included?

The practice set for Predicting What Comes Next: Exploring Sequences and Progressions mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Predicting What Comes Next: Exploring Sequences and Progressions for full coverage.

How many practice questions are there for Predicting What Comes Next: Exploring Sequences and Progressions?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Predicting What Comes Next: Exploring Sequences and Progressions Class 9 Mathematics Practice Questions with Answers

easy

Formulate an explicit formula for the

n^{th}

term of the sequence 2, 5, 10, 17, 26, ... and justify why this sequence is not an AP or a GP.

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easy

A small theater has 20 seats in the first row, 23 seats in the second row, 26 seats in the third row, and this pattern continues. Calculate the number of seats in the 15th row.

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easy

Define a sequence.

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easy

Define a Geometric Progression (GP).

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easy

Calculate the 12th term of the arithmetic progression:

-5, -1, 3, 7, ...

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easy

Create a sequence that is neither an AP nor a GP, for which the explicit formula is a quadratic in

n

. Formulate the rule, then use it to find the 15th term of your created sequence.

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easy

Explain the difference between a finite sequence and an infinite sequence. Provide one original example for each.

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easy

A sequence is defined by the recursive rule

t_1 = 5

and

t_n = t_{n-1} - 4

for

n \geq 2

. Calculate the first four terms of this sequence.

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easy

A student claims that if you take any Arithmetic Progression and square each term, the resulting sequence is also an Arithmetic Progression. Critique this claim by providing a counterexample and a justification.

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easy

A sequence is defined by the explicit rule

t_n = n^2 - 3n

. Calculate the value of the 5th term.

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easy

Define an Arithmetic Progression (AP).

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easy

Formulate a recursive rule for a sequence where the first term is 5 and each subsequent term is the cube of the previous term.

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easy

Calculate the common ratio for the geometric progression:

16, -8, 4, -2, ...

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medium

Explain the meaning of the 'common ratio' in a Geometric Progression. Provide an example of a GP and identify its common ratio.

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medium

Examine if the sequence

1, 1, 2, 3, 5, ...

(the Fibonacci sequence starting from

t_2

) is an arithmetic progression or a geometric progression. Justify your answer.

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medium

Justify whether the sequence defined by the explicit rule

t_n = n^2 - (n-1)^2

for

n \ge 1

is an Arithmetic Progression, a Geometric Progression, or neither.

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medium

Design a real-world problem involving compound interest that can be modeled by a geometric progression. Your problem must: a) Clearly state an initial investment, an annual interest rate, and a target amount. b) Formulate the explicit GP rule for the value of the investment after

n

years. c) Propose a question that asks for the minimum number of years to reach the target amount. d) Provide a complete, step-by-step solution to the problem you designed.

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medium

Explain the primary advantage of having an explicit formula for a sequence compared to a recursive formula.

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medium

Explain the relationship between the sequence of triangular numbers and the sum of natural numbers. Recall the explicit formula for the

n^{\text{th}}

triangular number and explain what each part of the formula represents.

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medium

What does the notation

t_n

represent in the context of a sequence?

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medium

A rare collectible's value is initially ₹2,00,000. Expert A proposes its value decreases by a fixed ₹15,000 each year. Expert B proposes it decreases by 8% of its value from the previous year. Evaluate which model represents an AP and which a GP. Formulate the explicit rule for each model and calculate the collectible's value after 4 years for both.

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medium

A person takes a loan and repays it in monthly installments. The first installment is ₹2,000, and each subsequent installment increases by ₹250. (a) Write the sequence of the first four installments and identify the type of progression. (b) Calculate the amount of the 12th installment. (c) Write the explicit formula for the

n^{\text{th}}

installment.

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medium

A sequence is defined by the explicit rule

t_n = 3 \times 2^{n-1}

. Another sequence is defined by

s_n = 3 + 2(n-1)

. Calculate the first four terms of each sequence and compare their growth.

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medium

The 4th term of an arithmetic progression is 11 and its 9th term is 26. Determine the first three terms of the AP.

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medium

Formulate an explicit formula for the sequence representing the sum of the first

n

odd natural numbers (i.e.,

1, 1+3, 1+3+5, \ldots

). Justify your formula by treating the sum as the sum of an AP.

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medium

A student claims that the sequence

a, a, a, a, \ldots

(where

a \neq 0

) is both an AP and a GP. Critique this claim and provide a mathematical justification for your conclusion.

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medium

Justify why the points representing the terms of any Arithmetic Progression, when plotted as ordered pairs

(n, t_n)

, must lie on a straight line.

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medium

Describe the recursive rule for the Virahānka-Fibonacci sequence, including the starting terms.

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medium

Describe the key differences between an Arithmetic Progression (AP) and a Geometric Progression (GP). Your description should include how consecutive terms are related in each, the name of the constant value that defines the progression, and the general form of the

n^{\text{th}}

term.

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medium

The number of algae in a pond triples every day. If there are 50 algae on day 1, calculate the number of algae on day 5. Also, write the explicit formula for the number of algae on day 'n'.

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medium

Recall the explicit formula for the

n^{\text{th}}

term of an Arithmetic Progression.

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medium

For the sequence defined by the recursive rule

s_1 = 2

and

s_n = 3s_{n-1} + 1

for

n \geq 2

, calculate the 4th term and examine if 178 is a term in this sequence.

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medium

Which term of the geometric progression

3, 12, 48, ...

is 3072?

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medium

Explain the meaning of the 'common difference' in an Arithmetic Progression. Provide an example of an AP and identify its common difference.

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hard

The sum of the first

n

terms of a sequence is given by the formula

S_n = 3n^2 - 2n

. Justify that this sequence is an AP and formulate its explicit rule

t_n

.

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hard

Prove that for any Arithmetic Progression, if its distinct

p^{th}

,

q^{th}

, and

r^{th}

terms are in Geometric Progression, then the common ratio (

R

) of that GP is given by

R = \frac{r-q}{q-p}

.

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hard

Derive the general formula for the sum of the first

n

terms of an Arithmetic Progression,

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

. Your derivation must use the method of writing the sum forwards and backwards and then adding the two expressions.

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hard

Summarize the patterns observed in the Sierpiński triangle fractal as described in the text. Explain how the number of black triangles forms one type of sequence and how the area of the black region forms another type of sequence. Name the type of progression for each.

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hard

Consider the Sierpiński carpet fractal where a square of area 1 is divided into 9 smaller squares and the central one is removed. This process is repeated for the remaining squares at each stage. (a) Calculate the number of shaded squares at Stage 3. Write the explicit formula for the number of shaded squares at Stage

n

. (b) Calculate the total area of the shaded region at Stage 3. Write the explicit formula for the shaded area at Stage

n

. (c) Compare the two sequences for the number of squares and the area. What do you observe as

n

becomes very large?

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hard

Evaluate if a sequence with at least three distinct terms can be both an Arithmetic Progression and a Geometric Progression simultaneously. Justify your answer mathematically.

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hard

Identify which of the following sequences are Arithmetic Progressions. Justify your answer by stating the common difference if it exists. (i)

2, 4, 8, 16, \ldots

(ii)

10, 7, 4, 1, \ldots

(iii)

1, 1, 2, 3, 5, \ldots

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hard

Identify which of the following sequences are Geometric Progressions. Justify your answer by stating the common ratio if it exists. (i)

1, 4, 7, 10, \ldots

(ii)

81, 27, 9, 3, \ldots

(iii)

5, -10, 20, -40, \ldots

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hard

The sum of the first three terms of a geometric progression is 39, and their product is 729. Solve for the first term and the common ratio of the GP. (Hint: Let the three terms be

\frac{a}{r}, a, ar

)

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hard

Consider a fractal construction starting with a single square (Stage 0). To get to Stage 1, the square is divided into a 3x3 grid, and only the four corner squares are kept. This process is repeated on each of the remaining squares for subsequent stages. Formulate both a recursive rule and an explicit rule for the number of shaded squares at stage

n

.

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hard

Calculate the sum of the first 20 terms of the arithmetic progression 2, 5, 8, ... using the method of reversing the sum.

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Predicting What Comes Next: Exploring Sequences and ProgressionsClass 9 Mathematics Practice Questions