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

1. Let the sequence be 1×2, 3×2^{2}, 5×2^{3}, 7×2^{4}, 9×2^{5}……… then this sequence is

a) An airthmetic sequence

b) A geometic progression

c) Airthmetico-geometric progression

d) None of the mentioned

View Answer

Explanation: If a

_{1}, a

_{2}……… are in AP and b

_{1}, b

_{2}………. are in GP then a

_{2}b

_{2}, a

_{2}b

_{2},……… are in AGP.

2. Let the sequence be 1×2, 3×2^{2}, 5×2^{3}, 7×2^{4}, 9×2^{5}……… then the next term of this AGP is given by:

a) 10×26

b) 10×27

c) 11×26

d) None of the mentioned

View Answer

Explanation: Since here a

_{1}, a

_{2}……… are in AP and b

_{1}, b

_{2}………. are in GP then a

_{2}b

_{2}, a

_{2}b

_{2},……… are in AGP thus a

_{n}= 11 and b

_{n}= 2

^{6}.

3. The sum of the first n natural numbers is given by:

a) n(n+1)/2

b) n(n-1)/2

c) n^{2}(n+1)/2

d) None of the mentioned

View Answer

Explanation: 1 + 2 + 3 + 4 +……n = (n/2)(1 + n) Since this is AP.

4. The sum of square of the first n natural numbers is given by:

a) n(n+1)(2n+1)/6

b) n(n-1)/2(2n+1)

c) n^{2}(n+1)(2n+1)/6

d) None of the mentioned

View Answer

Explanation: 1

^{2}+ 2

^{2}+ 3

^{2}+ 4

^{2}+……n

^{2}= n(1+n)(2n+1)/6.

5. The sum of cubes of the first n natural numbers is given by:

a) {n(n+1)/2}^{2}

b) {n(n-1)/2}^{2}

c) {n2(n+1)/2}^{2}

d) None of the mentioned

View Answer

Explanation: 1

^{3}+ 2

^{3}+ 3

^{3}+ 4

^{3}+……+ n

^{3}= {n(n+1)/2}

^{2}.

6. State whether the given statement is true or false

The series 1, 1, 1, 1, 1…….. is not an AGP.

a) True

b) False

View Answer

Explanation: Since 1, 1, 1, 1, 1…….. is in Ap and in Gp as well, Therfore the given sequence is also a AGP.

7.If in a AGP the common ratio of GP is 1 then that sequence becomes a AP sequence.

a) True

b) False

View Answer

Explanation: In AGP sequence if r = 1, then terms are ab,(a+d)b,(a+2d)b…. and so on thus it is AP with common differnce bd.

8. The sequence 1, 1, 1, 1, 1…. is :

a) Absolutely summable

b) Is not absolutely summable

c) Can’t say

d) None of the mentioned

View Answer

Explanation: For limit n tending to infinitythe sum also tends to infinity and thus it is not summable.

9. Which of the following is a Triangular number series :

a) 1, 3, 6, 9, 12, 15…..

b) 1, 3, 6, 10, 15, 21……

c) 1, 6, 12, 18, 24…..

d) none of the mentioned

View Answer

Explanation: In triangular number sequence ith term is previous term+i,with first term as 1.

10.Which of the following is a fibonacci series:

a) 0, 1, 2, 3, 4…….

b) 0, 1, 1, 2, 3, 5……

c) 10, 12, 14, 16…….

d) none of the mentioned

View Answer

Explanation: Fibonacci series is formed by adding previous two term starting from 0 and 1.

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

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