Predicting What Comes Next Exploring Sequences and Progressions Class 9 MCQ Maths Chapter 8

Explore numerous Class 9 Maths MCQ and Ganita Manjari Class 9 Maths Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions MCQ Questions Online Test with Answers provided with detailed solutions by looking below.

MCQ on Predicting What Comes Next Exploring Sequences and Progressions Class 9

Class 9 Maths Predicting What Comes Next Exploring Sequences and Progressions MCQ

Choose the correct option from the given options:

Question 1.
n^th term of a sequence is defined as a_n = 4n – 1. Its tenth term is:
(a) 10
(b) 40
(c) 39
(d) 14
Solution:
(c) 39

Explanation:
Here, a_n = 4n – 1,
To get its tenth term we put n – 10 in the given expression for the nth term.
So, we get a₁₀ = 4 × 10 – 1 = 40 – 1 = 39.

Question 2.
The sum of first 10 natural numbers is:
(a) 10
(b) 55
(c) 45
(d) 35
Solution:
(b) 55

Explanation:
Since, the sum of first n natural numbers is given by S_n = \(\frac{n(n+1)}{2}\)
To get the sum of first 10 natural numbers we put n = 10 in S_n = \(\frac{n(n+1)}{2}\), we obtain
S₁₀ = \(\frac{10 \times(10+1)}{2}=\frac{10 \times 11}{2}\) = 55

Question 3.
12th term of the sequence of the triangular numbers is:
(a) 10
(b) 55
(c) 45
(d) 78
Solution:
(d) 78

Explanation:
Since, the nth term of the sequence of the triangular numbers is the sum of the first n natural numbers. Thus t_n = \(\frac{n(n+1)}{2}\).
To get the 12th term of this sequence we put n = 12 in t_n = \(\frac{n(n+1)}{2}\), we obtain
t₁₂ = \(\frac{12 \times(12+1)}{2}=\frac{12 \times 13}{2}\) = 78

Question 4.
The common difference of the AP: 2, 7, 12, 17 is:
(a) 5
(b) 2
(c) 4
(d) -5
Solution:
(a) 5

Explanation:
Since, d= a_n – a_n-1
Hence, d = 12 – 7 = 5
So, its common difference = 5.

Question 5.
The third term of the recursive sequence given by the recursive rule
u₁ = 1, u_n = 2u_n-1 + 3 for n > 2 is:
(a) 5
(b) 13
(c) 29
(d) 1
Solution:
(b) 13

Explanation:
Since, u₁ = 1, u_n = 2u_n-1 +3 for n > 2
Hence, u₂ = 2u_2-1 + 3 = 2u₁ + 3 = 2 × 1 + 3 = 2 + 3 = 5
u₃ = 2u_3-1 + 3 = 2 u₂ + 3 = 2 × 5 + 3 = 10 + 3 = 13
So, the third term = 13.

Predicting What Comes Next Exploring Sequences and Progressions MCQ Class 9

Question 6.
The sequence 34, 30, 26, 22, … is a/an:
(a) HP
(b) GP
(c) AP
(d) None of these
Solution:
(c) AP

Explanation:
Here, a₁ = 34, a₂ = 30, a₃ = 26, a₄ = 22,…
Hence, a₂ – a₁ = 30 – 34 = – 4,
a₃ – a₂ = 26 – 30 = – 4,
a₄ – a₃ = 22 – 26 = – 4,
Since, difference between any two consecutive terms is the same throughout.
So, the given sequence is an AP.

Question 7.
The sequence 4, 8, 16, 32, … is a/an:
(a) HP
(b) GP
(c) AP
(d) None of these
Solution:
(b) GP

Explanation:
Here, a₁ = 4, a₂ = 8, a₃ = 16, a₄ = 32,…
Hence, a₂ ÷ a₁ = 8 ÷ 4 = 2,
a₃ ÷ a₂ = 16 ÷ 8 = 2,
a₄ ÷ a₃ = 32 ÷ 16 = 2,
Since, ratio of any two consecutive terms is the same throughout.
So, the given sequence is a GP.

Question 8.
Second term of the sequence given by the recursive rule s₁ = 3, s_n = s_n-1 (s_n-1 – 1) for n ≥ 2
(a) \(\frac{-1}{6}\)
(b) \(\frac{1}{6}\)
(c) -6
(d) 6
Solution:
(d) 6

Explanation:
Since, s₁ = 3, s_n = s_n-1s_n-1 – 1 for n ≥ 2
Hence, s₂ = s_2-1s_2-1 – 1
⇒ s₂ = s₁(s₁ – 1) = 3(3 – 1) = 3 × 2 = 6
So, the second term = 6.

Question 9.
The next term of the sequence 2, 2. 75, 3. 5, 4. 25, 5,…
(a) 5.25
(b) 5.50
(c) 5.75
(d) 6
Solution:
(c) 5.75

Explanation:
Given sequence is: 2,2.75,3.5,4.25,5,…
We can notice that it is an AP and its common difference is 5 – 4.25 = 0.75
So, the next term = last given term + common difference = 5 + 0.75 = 5.75.

Question 10.
The next term of the sequence 2,8,32,128,…
(a) 512
(b) 256
(c) 1024
(d) 384
Solution:
(a) 512

Explanation:
Given sequence is: 2, 8, 32, 128,…
We can notice that it is a GP and its common ratio is \(\frac{128}{32}\) = 4
So, the next term = last given term × common ratio = 128 × 4 = 512.

Question 11.
n^th term of a sequence is defined as a_n = 2n – 1. Its sixth term is:
(a) 10
(b) 20
(c) 11
(d) 12
Solution:
(c) 11

Question 12.
The sum of first 20 natural numbers is:
(a) 210
(b) 55
(c) 245
(d) 135
Solution:
(a) 210

Question 13.
10^th term of the sequence of the triangular numbers is:
(a) 10
(b) 55
(c) 45
(d) 35
Solution:
(b) 55

Question 14.
The common difference of the AP: 12,10,8,… is:
(a) 5
(b) 2
(c) -2
(d) -5
Solution:
(c) -2

Question 15.
The fourth term of the recursive sequence given by the recursive rule
u₁ = 1, u_n = 2u_n-1 + 3 for n ≥ 2 is:
(a) 5
(b) 13
(c) 29
(d) 1
Solution:
(c) 29

Question 16.
The sequence 35, 45, 55, 65,… is a/an:
(a) HP
(b) GP
(c) AP
(d) None of these
Solution:
(c) AP

Question 17.
The sequence 3, 9, 27, 81, … is a/an:
(a) HP
(b) GP
(c) AP
(d) None of these
Solution:
(b) GP

Question 18.
Third term of the sequence given by the recursive rule s₁ = 3, s_n = s_n-1(s_n-1 – 1) for n > 2 is:
(a) \(\frac{-1}{30}\)
(b) \(\frac{1}{3}\)
(c) -30
(d) 30
Solution:
(d) 30

Question 19.
The next term of the sequence \(\frac{1}{3}, \frac{2}{3}\), 1, \(\frac{4}{3}\), …………….. is:
(a) \(\frac{5}{3}\)
(b) 2
(c) \(\frac{3}{4}\)
(d) \(\frac{-2}{3}\)
Solution:
(a) \(\frac{5}{3}\)

Question 20.
The next term of the sequence 2, 1, \(\frac{1}{2}, \frac{1}{4}\) …………..
(a) \(\frac{1}{512}\)
(b) \(\frac{1}{256}\)
(c) \(\frac{1}{8}\)
(d) \(\frac{1}{16}\)
Solution:
(c) \(\frac{1}{8}\)

Predicting What Comes Next Exploring Sequences and Progressions Class 9 Assertion and Reason Questions

Direction: A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following options.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

Question 1.
Assertion (A): In the AP: 2, 5, 8, 11, …, the common difference is 3.
Reason (R): d = a_n – a_n-1
Solution:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:
Given AP is: 2, 5, 8, 11, …
So, we can get its common difference by d = 11 – 8 = 3 or, 8 – 5 = 3 or 5 – 2 = 3.
Hence, common difference = 3.
Hence, Assertion (A) is true.
In an AP, the common difference is obtained by: d = a_n – a_n-1
Thus, Reason (R) is true and Reason (R) is the correct explanation of Assertion (A).

Question 2.
Assertion (A): In the GP: 2, 10, 50, 250, …, the common ratio is 5.
Reason (R): Common ratio of a GP is given by r = a_n ÷ a_n-1.
Ans.
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:
Given GP is: 2, 10, 50, 250, …
So, we can get its common ratio by r = 50 ÷ 10 = 5.
Hence, common ratio = 5.
Hence, Assertion (A) is true.
In a GP, the common ratio is obtained by: r = a_n ÷ a_n-1
Thus, Reason (R) is true and Reason (R) is the correct explanation of Assertion (A).

Question 3.
Assertion (A): 2, 1, \(\frac{1}{2}\) are three terms of a GP.
Reason (R): In a GP, each term is a constant multiple of the previous term.
Solution:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Question 4.
Assertion (A): In an AP: 2, 4, 6, 8,… the n^th term is 2n.
Reason (R): In an AP each term differ from its previous term by a constant.
Solution:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Question 5.
Assertion (A): 2, x, \(\frac{1}{2}\) is in GP, if x = 1.
Reason (R): 10, 20, 40 are three terms of an AP.
Solution:
(c) Assertion (A) is true but Reason (R) is false.