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.

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.

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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