Arithmetic Sequences - Discrete Mathematics Questions and Answers

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

1. Let the sequence be 1, 3, 5, 7, 9……… then this sequence is ____________
a) An arithmetic sequence
b) A geometric progression
c) A harmonic sequence
d) None of the mentioned
View Answer

Answer: a
Explanation: The difference in any term with the previous term is same.

2. In the given AP series find the number of terms?

5, 8, 11, 14, 17, 20.........50.

a) 11
b) 13
c) 15
d) None of the mentioned
View Answer

Answer: d
Explanation: n^th term = first_term + (number_of_terms – 1)common_differnce., 50 = 5 + (n-1)3, n=16.

3. In the given AP series the term at position 11 would be?

5, 8, 11, 14, 17, 20.........50.

a) 35
b) 45
c) 25
d) None of the mentioned
View Answer

Answer: a
Explanation: n^th term = a + (n – 1)d, n^th term = 5+(11-1)3 = 35.

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4. For the given Arithmetic progression find the position of first negative term?

50, 47, 44, 41,............

a) 17
b) 20
c) 18
d) None of the mentioned
View Answer

Answer: c
Explanation: Let n^th term=0, the next term would be first negative term.
0 = 50 + (n-1) – 3, n = 17.66.. therfore at n = 18 the first negative term would occur.

5. For the given Arithmetic progression find the first negative term?

50, 47, 44, 41,............

a) -1
b) -2
c) -3
d) None of the mentioned
View Answer

Answer: a
Explanation: Let n^th term = 0, the next term would be first negative term.
0 = 50 +(n-1)- 3, n = 17.66.. therfore at n=18 the first negative term would occur. N^th term = 50 + (18-1) – 3 = -1.

6. A series can either be AP only or GP only or HP only but not all at the same time.
a) True
b) False
View Answer

Answer: b
Explanation: 1, 1, 1, 1, 1…….. is AP, GP and HP series.

7. In the given Arithmetic progression, ’25’ would be a term in it.

5, 8, 11, 14, 17, 20.........50.

a) True
b) False
View Answer

Answer: b
Explanation: n^th term = a + (n-1)d, 25 = 5 + (n-1)3, n = 23/3, n = 7.666 not an integer. Thus 25 is not a term in this series.

8. Which of the following sequeces in AP will have common difference 3, where n is an Integer?
a) a_n = 2n² + 3n
b) a_n = 2n² + 3
c) a_n = 3n² + 3n
d) a_n = 5 + 3n
View Answer

Answer: d
Explanation: a_n = 5 + 3n it is a linear expression with coefficient of as 3. So it is AP with common difference 3.

9. If a, b, c are in AP then relation between a, b, c can be _________
a) 2b = 2a + 3c
b) 2a = b + c
c) 2b = a + c
d) 2c = a + c
View Answer

Answer: c
Explanation: The term b should be the airthmetic mean of of term a and c.

10. Let the sum of the 3 consecutive terms in AP be 180 then midlle of those 3 terms would be ________
a) 60
b) 80
c) 90
d) 179
View Answer

Answer: a
Explanation: Let a₁, b₁, c₁ be three terms, then a₁ + b₁ + c₁ = 180, a₁ + c₁ = 2b₁(A M property), 3b₁ = 180, b₁=60.

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