Sequences & Summations - Discrete Mathematics Questions and Answers

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Sequences and Summations”.

1. For the sequence 1, 7, 25, 79, 241, 727 … simple formula for {a_n} is ____________
a) 3ⁿ⁺¹ – 2
b) 3ⁿ – 2
c) (-3)ⁿ + 4
d) n² – 2
View Answer

Answer: b
Explanation: The ratio of consecutive numbers is close to 3. Comparing these terms with the sequence of {3ⁿ} which is 3, 9, 27 …. Comparing these terms with the corresponding terms of sequence {3ⁿ} and the nth term is 2 less than the corresponding power of 3.

2. For the sequence 0, 1, 2, 3 an is ____________
a) ⌈n/2⌉+⌊n/2⌋
b) ⌈n/2⌉+⌈n/2⌉
c) ⌊n/2⌋+⌊n/2⌋
d) ⌊n/2⌋
View Answer

Answer: a
Explanation: Expand the sequence ⌈n/2⌉+⌊n/2⌋ where a1 is ⌊0.5⌋+⌈0.5⌉ = 1+0 = 1, a2 is ⌊1⌋+⌈1⌉ = 1 + 1 = 2 and so on.

3. The value of∑(k=50)¹⁰⁰ k² is __________
a) 338, 350
b) 297, 900
c) 297, 925
d) 290, 025
View Answer

Answer: c
Explanation: Using the formula. ∑(k=1)ⁿ k² = (n(n + 1)(2n + 1)) / 6.

4. The sets A and B have same cardinality if and only if there is ___________ from A to B.
a) One-to-one
b) One-to-many
c) Many-to-many
d) Many-to-one
View Answer

Answer: a
Explanation: If there is one-to-one correspondence then they have same cardinality.

5. For the sequence a_n = ⌊√2n+ 1/2⌋, a₇is ____________
a) 1
b) 7
c) 5
d) 4
View Answer

Answer: d
Explanation: a₇ = ⌊√14+1/2⌋ which is ⌊4.24⌋ = 4.

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6. The value of ∑(i=1)³ ∑(h=0)² i is _________
a) 10
b) 17
c) 15
d) 18
View Answer

Answer: d
Explanation: The value of ∑(i=1)³ ∑(h=0)² i = 1+1+1+2+2+2+3+3+3 = 18.

7. For the sequence a_n = 6. (1/3)ⁿ, a₄ is _________
a) 2/25
b) 2/27
c) 2/19
d) 2/13
View Answer

Answer: b
Explanation: Put n = 4 in the sequence.

8. The value of ∑(i=0)⁴i! is __________
a) 32
b) 30
c) 34
d) 35
View Answer

Answer: c
Explanation: First five term of the sequence n! is given by 1, 1, 2, 6, 24.

9. Set of all integers is counter.
a) True
b) False
View Answer

Answer: a
Explanation: There is one-to-one correspondence between set of positive integers and set of all integers.

10. The value of ∏(k=1)¹⁰⁰(-1) ^k is _________
a) 0
b) 1
c) -1
d) 2
View Answer

Answer: b
Explanation: The product of a₁, a₂, a₃ …… a_n is represented by ∏(i=1)ⁿ a_i.

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