This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses 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
View Answer
Explanation: 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
View Answer
Explanation: Since here a1, a2……… are in AP and b1, b2………. are in GP then a2b2, a2b2,……… are in AGP thus an = 11 and bn = 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
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) n2(n+1)(2n+1)/6
d) None of the mentioned
View Answer
Explanation: 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
View Answer
Explanation: 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
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.
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