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

1. Let the sequence be 2, 8, 32, 128,……… 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 ratio of any term with previous term is same.

2. In the given Geometric progression find the number of terms

32, 256, 2048, 16384,………,2^{50}.

a) 11

b) 13

c) 15

d) None of the mentioned

View Answer

Explanation: n

^{th}term = first term(ratio

^{n – 1})., 2

^{50}= 2

^{5}(2

^{3(n-1)}), n=15. This implies 16

^{th}term.

3. In the given Geometric progression the term at position 11 would be

32, 256, 2048, 16384,………,2^{50}.

a) 2^{35}

b) 2^{45}

c) 35

d) None of the mentioned.

View Answer

Explanation: n

^{th}term = first term(ratio

^{n – 1})., g

_{n}= 2

^{5}(2

^{3(n-1)}), n=11. This implies 2

^{35}.

4. For the given Geometric progression find the position of first fractional term?

2^{50}, 2^{47}, 2^{44},………

a) 17

b) 20

c) 18

4) None of the mentioned.

View Answer

Explanation: Let n

^{th}term=1 ,the next term would be first fractional term.

G

_{n}= 1 = 2

^{50}(2

^{3(-n+1)}), n=17.66.. therfore at n = 18 the first fractional term would occur.

5. For the given geometric progression find the first fractional term?

2^{50}, 2^{47}, 2^{44},………

a) 2^{-1}

b) 2^{-2}

c) 2^{-3}

4) None of the mentioned.

View Answer

Explanation: Let n

^{th}term=1 ,the next term would be first fractional term.

G

_{n}= 1 = 2

^{50}( 2

^{3(-n+1)}), n=17.66.. therefore at n=18 the first fractional term would occur.G

_{n}= 2

^{50}( 2

^{3(-n+1)}), G

_{18}= 2

^{-1}.

6. State whether the given statement is true or false

1, 1, 1, 1, 1…….. is a GP series .

a) True

b) False

View Answer

Explanation: The ratio of any term with previous term is same.

7. In the given Geometric progression, ‘2^{25}‘ would be a term in it.

32, 256, 2048, 16384,………,2^{50}.

a) True

b) False

View Answer

Explanation: n

^{th}term = first term(ratio

^{n – 1})., g

_{n}= 2

^{25}= 2

^{5}(2

^{3(n-1)}), n=23/3, n=7.666 not an integer. Thus 2

^{25}is not a term in this series.

8. Which of the following sequeces in GP will have common ratio 3,where n is an Integer?

a) g_{n} = 2n^{2} + 3n

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

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

d) g_{n} = 6(3^{n-1})

View Answer

Explanation: g

_{n}= 6( 3

^{n-1}) it is a geometric expression with coefficient of constant as 3

^{n-1}.So it is GP with common ratio 3.

9. If a, b, c are in GP then relation between a, b, c can be

a) 2b = 2a + 3c

b) 2a = b+c

c) b =(ac)^{1/2}

d) 2c = a + c

View Answer

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

10. Let the multiplication of the 3 consecutive terms in GP be 8 then midlle of those 3 terms would be:

a) 2

b) 3

c) 4

d) 179

View Answer

Explanation: Let a, b, c be three terms ,then a/r * a * ar = 8, b = (ac)

^{1/2}(G M property), b

^{3}= 8, b = 2.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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