Geometric Sequences - Discrete Mathematics Questions and Answers

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 arithmetic sequence
b) A geometic progression
c) A harmonic sequence
d) None of the mentioned
View Answer

Answer: b
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,.........,2⁵⁰.

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

Answer: d
Explanation: n^th term = first term(ratio^{n – 1})., 2⁵⁰ = 2⁵(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,.........,2⁵⁰.

a) 2³⁵
b) 2⁴⁵
c) 35
d) None of the mentioned
View Answer

Answer: a
Explanation: n^th term = first term(ratio^{n – 1})., g_n = 2⁵(2^3(n-1)), n=11. This implies 2³⁵.

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

2⁵⁰, 2⁴⁷, 2⁴⁴,.........

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

Answer: c
Explanation: Let n^th term=1, the next term would be first fractional term.
G_n = 1 = 2⁵⁰(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?

2⁵⁰, 2⁴⁷, 2⁴⁴,.........

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

Answer: a
Explanation: Let n^th term=1, the next term would be first fractional term.
G_n = 1 = 2⁵⁰( 2 ^3(-n+1)), n=17.66. Therefore at n=18 the first fractional term would occur. G_n = 2⁵⁰( 2 ^3(-n+1)), G₁₈ = 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

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

7. In the given Geometric progression, ‘2²⁵‘ would be a term in it.

32, 256, 2048, 16384,.........,2⁵⁰.

a) True
b) False
View Answer

Answer: b
Explanation: n^th term = first term(ratio^{n – 1})., g_n = 2²⁵ = 2⁵ (2 ^3(n-1)), n=23/3, n=7.666 not an integer. Thus 2²⁵ 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 = 2n² + 3n
b) g_n = 2n² + 3
c) g_n = 3n² + 3n
d) g_n = 6(3^n-1)
View Answer

Answer: d
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

Answer: c
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

Answer: a
Explanation: Let a, b, c be three terms, then a/r * a * ar = 8, b = (ac)^1/2 (G M property), b³ = 8, b = 2.

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