250+ TOP MCQs on Special Sequences and Answers

Discrete Mathematics Multiple Choice Questions on “Special Sequences”.

1. Let the sequence be 1×2, 3×2², 5×2³, 7×2⁴, 9×2⁵……… then this sequence is _________
a) An arithmetic sequence
b) A geometic progression
c) Arithmetico-geometric progression
d) None of the mentioned

Answer: c
Clarification: If a₁, a₂……… are in AP and b₁, b₂………. are in GP then a₂b₂, a₂b₂,……… are in AGP.

2. Let the sequence be 1×2, 3×2², 5×2³, 7×2⁴, 9×2⁵……… then the next term of this AGP is given by _________
a) 10×26
b) 10×27
c) 11×26
d) None of the mentioned

Answer: c
Clarification: Since here a₁, a₂……… are in AP and b₁, b₂………. are in GP then a₂b₂, a₂b₂,……… are in AGP thus a_n = 11 and b_n = 2⁶.

3. The sum of the first n natural numbers is given by _________
a) n(n+1)/2
b) n(n-1)/2
c) n²(n+1)/2
d) None of the mentioned

Answer: a
Clarification: 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) n²(n+1)(2n+1)/6
d) None of the mentioned

Answer: a
Clarification: 1² + 2² + 3² + 4² +……n² = 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

Answer: a
Clarification: 1³ + 2³ + 3³ + 4³ +……+ n³ = {n(n+1)/2}².

6. The series 1, 1, 1, 1, 1…….. is not an AGP.
a) True
b) False

Answer: b
Clarification: 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

Answer: a
Clarification: 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

Answer: b
Clarification: 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

Answer: b
Clarification: 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

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