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) 3^{n+1} – 2

b) 3^{n} – 2

c) (-3)^{n} + 4

d) n^{2} – 2

View Answer

Explanation: The ratio of consecutive numbers is close to 3. Comparing these terms with the sequence of {3

^{n}} which is 3, 9, 27 …. Comparing these terms with the corresponding terms of sequence {3

^{n}} 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

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▒k^{2} is ________.

a) 338,350

b) 297,900

c) 297,925

d) 290,025

View Answer

Explanation: Using the formula .∑_(k=1)^n▒k

^{2}= (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

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

5. For the sequence a_{n} = ⌊√2n+ 1/2⌋, a_{7}is ____________.

a) 1

b) 7

c) 5

d) 4

View Answer

Explanation: a

_{7}= ⌊√14+1/2⌋ which is ⌊4.24⌋ = 4.

6. The value of ∑_(i=1)^3▒∑_(h=0)^2▒i is ______.

a) 10

b) 17

c) 15

d) 18

View Answer

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}, a_{4} is ______.

a) 2/25

b) 2/27

c) 2/19

d) 2/13

View Answer

Explanation: Put n = 4 in the sequence.

8. The value of ∑_(i=0)^4▒i! is ___.

a) 32

b) 30

c) 34

d) 35

View Answer

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

9. Set of all integers is counter. Is it True or False?

a) True

b) False

View Answer

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

Explanation: The product of a

_{1}, a

_{2}, a

_{3}…… a

_{n}is represented by ∏_(i=1)^n▒a

_{i}.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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