Discrete Mathematics Multiple Choice Questions 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
Answer: a
Clarification: 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
Answer: d
Clarification: nth 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
Answer: a
Clarification: nth term = a + (n – 1)d, nth term = 5+(11-1)3 = 35.
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
Answer: c
Clarification: Let nth 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
Answer: a
Clarification: Let nth 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. Nth 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
Answer: b
Clarification: 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
Answer: b
Clarification: nth 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) an = 2n2 + 3n
b) an = 2n2 + 3
c) an = 3n2 + 3n
d) an = 5 + 3n
Answer: d
Clarification: an = 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
Answer: c
Clarification: 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
Answer: a
Clarification: Let a1, b1, c1 be three terms, then a1 + b1 + c1 = 180, a1 + c1 = 2b1(A M property), 3b1 = 180, b1=60.