250+ TOP MCQs on Geometric Sequences and Answers

Discrete Mathematics Multiple Choice Questions 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

Answer: b
Clarification: 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

Answer: d
Clarification: 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

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

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

Answer: c
Clarification: 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

Answer: a
Clarification: 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

Answer: a
Clarification: 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

Answer: b
Clarification: 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)

Answer: d
Clarification: 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

Answer: c
Clarification: 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

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