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 airthmetic sequence

b) A geometic progression

c) A harmonic sequence

d) None of the mentioned

View Answer

Explanation: The difference in any term with 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

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

Explanation: n

^{th}term = a + (n – 1)d, n

^{th}term = 5+(11-1)3 = 35.

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

50, 47, 44, 41,…………

a) 17

b) 20

c) 18

4) None of the mentioned.

View Answer

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 Airthmetic progression find the first negative term?

50, 47, 44, 41,…………

a) -1

b) -2

c) -3

4) None of the mentioned.

View Answer

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. State whether the given statement is true or false

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

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

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

5, 8, 11, 14, 17, 20………50.

a) True

b) False

View Answer

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} = 2n^{2} + 3n

b) a_{n} = 2n^{2} + 3

c) a_{n} = 3n^{2} + 3n

d) a_{n} = 5 + 3n

View Answer

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

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

Explanation: Let a

_{1}, b

_{1}, c

_{1}be three terms ,then a

_{1}+ b

_{1}+ c

_{1}= 180, a

_{1}+ c

_{1}= 2b

_{1}(A M property), 3b

_{1}= 180, b

_{1}=60.

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