CA Foundation Exam > CA Foundation Questions > If S be the sum, P the product and R the sum ...
Start Learning for Free
If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Sn and R-n.
- a)Arithmetic Mean
- b)Geometric Mean
- c)Harmonic Mean
- d)None
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
If S be the sum, P the product and R the sum of the reciprocals of n t...
Solution:
Let the first term of the G.P. be a and the common ratio be r.
Then, the n terms are a, ar, ar2, …, arn-1.
Sum of n terms of the G.P. can be calculated using the formula:
Sn = a(1-rn)/(1-r)
Product of n terms of G.P. can be calculated using the formula:
P = a^n rn(n-1)/2
Sum of reciprocals of n terms of G.P. can be calculated using the formula:
R = (1-a^n r-n)/(1-r)
We need to prove that P is the geometric mean of Sn and R-n.
Geometric mean of two numbers a and b is given by the formula:
GM = √ab
Let’s calculate the geometric mean of Sn and R-n.
GM = √(Sn × R-n)
= √[(a(1-rn)/(1-r)) × ((1-r)/(1-a^n r-n))]
= √[a(1-a^n r-n)/(1-a)(1-rn)]
= a^(n/2) rn(n-1)/4
= P^(1/2)
Therefore, we can see that P is the geometric mean of Sn and R-n.
Hence, the correct answer is option (B) Geometric Mean.
Let the first term of the G.P. be a and the common ratio be r.
Then, the n terms are a, ar, ar2, …, arn-1.
Sum of n terms of the G.P. can be calculated using the formula:
Sn = a(1-rn)/(1-r)
Product of n terms of G.P. can be calculated using the formula:
P = a^n rn(n-1)/2
Sum of reciprocals of n terms of G.P. can be calculated using the formula:
R = (1-a^n r-n)/(1-r)
We need to prove that P is the geometric mean of Sn and R-n.
Geometric mean of two numbers a and b is given by the formula:
GM = √ab
Let’s calculate the geometric mean of Sn and R-n.
GM = √(Sn × R-n)
= √[(a(1-rn)/(1-r)) × ((1-r)/(1-a^n r-n))]
= √[a(1-a^n r-n)/(1-a)(1-rn)]
= a^(n/2) rn(n-1)/4
= P^(1/2)
Therefore, we can see that P is the geometric mean of Sn and R-n.
Hence, the correct answer is option (B) Geometric Mean.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Similar CA Foundation Doubts
Top Courses for CA FoundationView all
If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer?
Question Description
If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer?.
If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer?.
Solutions for If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. then P is the ________ of Snand R-n.a)Arithmetic Meanb)Geometric Meanc)Harmonic Meand)NoneCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup