Predicting What Comes Next: Exploring Sequences and Progressions MCQs (Class 9 Maths, NCERT)
128 practice questions on Predicting What Comes Next: Exploring Sequences and Progressions, a chapter in the NCERT Class 9 Mathematics textbook, organised into 2 topics. Every question includes a written explanation. Pick a topic below, or try the samples first.
The term in position $n$ of a sequence is $7n - 2$. Which of these numbers is a term of the sequence?
A$60$
B$44$
C$50$
D$54$
Show answer and explanation
Correct answer: D - $54$
Solving $7n - 2 = 54$ gives $7n = 56$ and $n = 8$, so $54$ is the eighth term. For $50$, $60$ and $44$ the same working gives $7n = 52,\ 62$ and $46$, none of which is a multiple of $7$, so no position number fits them.
Q2
easy
The triangular numbers are the running sums of the natural numbers: $1$, then $1 + 2$, then $1 + 2 + 3$, and so on. What is the fifth triangular number?
A$21$
B$10$
C$12$
D$15$
Show answer and explanation
Correct answer: D - $15$
The fifth running sum is $1 + 2 + 3 + 4 + 5 = 15$. The value $10$ is the fourth triangular number and $21$ the sixth, each one place out, while $12$ appears nowhere in the list $1,\ 3,\ 6,\ 10,\ 15,\ 21$.
Q3
easy
An arithmetic progression has first term $6$ and common difference $4$. What is its $10$th term?
A$46$
B$38$
C$40$
D$42$
Show answer and explanation
Correct answer: D - $42$
Nine steps of $4$ from the first term give $6 + 9 \times 4 = 6 + 36 = 42$. The value $46$ takes ten steps instead of nine, $38$ takes only eight, and $40 = 10 \times 4$ leaves out the first term completely.
Q4
medium
A sequence is given by the rule $t_n = 4n + 1$. Assertion (A): $30$ is a term of this sequence. Reason (R): solving $4n + 1 = 30$ gives $n = 7.25$, which is not a position number.
ABoth A and R are true, and R is the correct explanation of A
BBoth A and R are true, but R is not the correct explanation of A
CA is true, but R is false
DA is false, but R is true
Show answer and explanation
Correct answer: D - A is false, but R is true
(R) is correct: $4n = 29$ gives $n = \frac{29}{4} = 7.25$, and positions are counted in natural numbers only. That very working shows $30$ never appears in the list, which sits between the terms $29$ and $33$, so (A) is false while (R) is true.
Q5
easy
Which of these is a finite sequence?
AThe square numbers $1,\ 4,\ 9,\ 16,\ \ldots$ written in increasing order
BThe odd numbers $1,\ 3,\ 5,\ 7,\ \ldots$ written in increasing order
CThe seven days of one particular week, numbered $1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7$
DAll the multiples of $4$, starting from $4$ and increasing
Show answer and explanation
Correct answer: C - The seven days of one particular week, numbered $1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7$
A sequence is finite when its list of terms comes to a stop, and the numbering of one week stops at $7$. The odd numbers, the multiples of $4$ and the square numbers all carry on without ever ending, so each of those lists is infinite.
Q6
easy
A recursive rule for a sequence tells you how to get a term from which piece of information?
AThe total of all the terms of the sequence
BOne or more of the terms that come before it
CIts position number alone
DThe very last term of the sequence
Show answer and explanation
Correct answer: B - One or more of the terms that come before it
A recursive rule builds each new term out of earlier ones, as in $t_n = t_{n-1} + 6$. A formula that uses only the position number is an explicit rule. A running total is not part of the rule at all, and an infinite sequence has no last term to work back from.
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