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 arithmetic sequence

b) A geometic progression

c) Arithmetico-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. 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, Therefore the given sequence is also an AGP.

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