Mathematics Questions and Answers – Geometric Progression(G.P.)

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Geometric Progression(G.P.)”.

1. A sequence is called ___________________ if an+1 = an * r.
a) arithmetic progression
b) geometric Progression
c) harmonic Progression
d) special Progression
View Answer

Answer: b
Explanation: A sequence is called geometric progression if an+1 = an * r where a1 is the first term and r is common ratio.
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2. What is nth term of a G.P.?
a) an = a + (n-1) d
b) an = a + (n) d
c) an = a*rn-1
d) an = a*rn
View Answer

Answer: c
Explanation: Since every term of an G.P. is r times the previous term.
i.e. an+1 = an * r = an-1 * r2 = ….. = a1 * rn
or an = a*rn-1

3. If first term of a G.P. is 20 and common ratio is 4. Find the 5th term.
a) 10240
b) 40960
c) 5120
d) 2560
View Answer

Answer: c
Explanation: Given, a=20 and r=4.
We know, an = arn-1
=>a5 = 20*44 = 20*256 = 5120.
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4. If a sequence is in the form 2*5n then which of the following may be the sequence?
a) Arithmetic progression
b) Geometric Progression
c) Harmonic Progression
d) Special Progression
View Answer

Answer: b
Explanation: If an = 2*5n then
a1 =10, a2 = 50, a3=250.
This is a geometric progression with first term 10 and common ratio 5.

5. If r=1 in a G.P. then what is the sum to n terms?
a) n*a
b) a/n
c) (n-1) a
d) (n+1) a
View Answer

Answer: a
Explanation: If a is the first term of G.P., then G.P. look like a, a, a, a, …………
Then sum to n terms becomes n*a.
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6. If a=3 and r=2 then find the sum up 5th term.
a) 95
b) 82
c) 93
d) 97
View Answer

Answer: c
Explanation: We know, Sn = a(rn-1)/(r-1)
Here a = 3, r = 2 and n = 5
S5 = 3 (25-1) / (2-1) = 3(32 -1) = 3*31 = 93.

7. In G.P. 4, 8, 16, 32, ………… find the sum up to 5th term.
a) 16
b) 64
c) 128
d) 124
View Answer

Answer: d
Explanation: In the given G.P., a=4 and r=8/4=2.
We know, Sn = a(rn-1)/(r-1)
=>S5 = 4(25-1) / (2-1) = 4*31 = 124.
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8. Which term of G.P. 25, 125, 625, …………. is 390625?
a) 5
b) 6
c) 7
d) 8
View Answer

Answer: c
Explanation: In the given G.P., a=25 and r = 125/25 = 5.
Given, an = 390625 => arn-1 = 390625
=>25*5n-1 = 390625
=> 5n-1 = 390625/25 = 15625 = 56
=> n-1 = 6 => n=7.

9. In a G.P., 5th term is 27 and 8th term is 729. Find its 11th term.
a) 729
b) 2187
c) 6561
d) 19683
View Answer

Answer: d
Explanation: Given, a5 = 27 and a8 = 729.
=>ar4 = 27 and ar7 = 729
On dividing we get, r3 = 27 => r=3
=> a=27 / (34) = 1/3
=>a11 = ar10 = (1/3) (310) = 39 = 19683.
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10. Find the sum of series 1+1/2 + 1/4 + ………. up to 6 terms.
a) 63/32
b) 32/63
c) 26/53
d) 53/26
View Answer

Answer: a
Explanation: Given series is G.P. with first term 1 and common ratio 1/2.
We know, Sn = a(1-rn)/(1-r) for r<1.
S6 = 1(1-(1/2)6) / (1-1/2) = (1-1/64) / (1/2) = 63*2/64 = 63/32.

11. How many terms of G.P. 2,4,8,16, …………… are required to give sum 254?
a) 4
b) 5
c) 6
d) 7
View Answer

Answer: d
Explanation: a=2 and r = 4/2 = 2.
We know, Sn = a(rn-1)/(r-1)
2(2n-1) / (2-1) = 254
=>2n-1 = 127 => 2n = 128 = 27
=> n=7.

12. The sum of first three terms of a G.P. is 21/2 and their product is 27. Find the common ratio.
a) 2
b) 1/2
c) 2 or 1/2
d) neither 2 nor 1/2
View Answer

Answer: c
Explanation: Let three terms be a/r, a, a*r.
Product = 27 => (a/r) (a) (a*r) = 27 => a3 = 27
=>a = 3.
Sum = 21/2 => (a / r + a + a*r) = 21/2 => a (1 / r + 1 + 1*r) = 21/2
=> (1 / r + 1 + 1*r) = (21/2)/3 = 7/2
=> (r2 + r + 1) = (7/2) r => r2 – (5/2) r + 1 = 0
=> r = 2 and 1/2.

13. The sum of first three terms of a G.P. is 21/2 and their product is 27. Which of the following is not a term of the G.P. if the numbers are positive?
a) 3
b) 2/3
c) 3/2
d) 6
View Answer

Answer: b
Explanation: Let three terms be a/r, a, a*r.
Product = 27 => (a/r) (a) (a*r) = 27 => a3 = 27
=>a = 3.
Sum = 21/2 => (a / r + a + a*r) = 21/2 => a (1 / r + 1 + 1*r) = 21/2
=> (1 / r + 1 + 1*r) = (21/2)/3 = 7/2
=> (r2 + r + 1) = (7/2) r => r2 – (5/2) r +1 = 0
=> r = 2 and 1/2.
Terms are 3/2, 3, 3*2 i.e. 3/2, 3, 6.

14. Which of the following is the geometric mean of 3 and 12.
a) 4
b) 6
c) 9
d) 10
View Answer

Answer: b
Explanation: We know, geometric mean of two numbers a and b is given by
G.M. = \(\sqrt{a*b}\)
So, G.M. of 3 and 12 is \(\sqrt{3*12} = \sqrt{36}\) = 6.

15. If three positive numbers are inserted between 4 and 512 such that the resulting sequence is a G.P., which of the following is not among the numbers inserted?
a) 256
b) 16
c) 64
d) 128
View Answer

Answer: d
Explanation: Let G.P. be 4, G1, G2, G3, 512.
=>a=4 and a5 = a*r4 = 512 => 4*r4 = 512 => r4 = 512/4 = 128 => r = 4.
G1 = a2 = a * r = 4*4 = 16.
G2 = G1 * r = 16 * 4 = 64.
G3 = G2 * r = 64*4 = 256.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter