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The product of three terms in G. P is 125/8, find G. M ?
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The product of three terms in G. P is 125/8, find G. M ?
Problem: The product of three terms in G. P is 125/8, find G. M?
Solution:
Let the three terms in the G.P be a, ar and ar^2
Then, their product is: a * ar * ar^2 = a^3r^3
Given, a^3r^3 = 125/8
Taking cube root on both sides, we get:
ar = (125/8)^(1/3) = 5/2
Also, ar^2 = (ar) * ar = (5/2) * ar = (5/2)^2
Therefore, r = ar/ar = (5/2) / 1 = 5/2
Now, we can find the second term of the G.P (i.e., ar) as 5/2.
Finally, we can find the G.M (i.e., geometric mean) of the three terms in the G.P as:
G.M = (a * ar * ar^2)^(1/3) = [a * (5/2) * (25/4)]^(1/3) = (125a/8)^(1/3)
Hence, we have found the G.M of the three terms in the G.P as (125a/8)^(1/3).
Conclusion: The G.M of the three terms in the G.P is (125a/8)^(1/3).
Solution:
Let the three terms in the G.P be a, ar and ar^2
Then, their product is: a * ar * ar^2 = a^3r^3
Given, a^3r^3 = 125/8
Taking cube root on both sides, we get:
ar = (125/8)^(1/3) = 5/2
Also, ar^2 = (ar) * ar = (5/2) * ar = (5/2)^2
Therefore, r = ar/ar = (5/2) / 1 = 5/2
Now, we can find the second term of the G.P (i.e., ar) as 5/2.
Finally, we can find the G.M (i.e., geometric mean) of the three terms in the G.P as:
G.M = (a * ar * ar^2)^(1/3) = [a * (5/2) * (25/4)]^(1/3) = (125a/8)^(1/3)
Hence, we have found the G.M of the three terms in the G.P as (125a/8)^(1/3).
Conclusion: The G.M of the three terms in the G.P is (125a/8)^(1/3).
Community Answer
The product of three terms in G. P is 125/8, find G. M ?
Let GM be a and common ratio be r
The terms will be a/r ,a ,ar
(a/r)(a)(ar)=125/8
a×a×a=125/8
a=5/2
The terms will be a/r ,a ,ar
(a/r)(a)(ar)=125/8
a×a×a=125/8
a=5/2
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The product of three terms in G. P is 125/8, find G. M ? 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 The product of three terms in G. P is 125/8, find G. M ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of three terms in G. P is 125/8, find G. M ?.
The product of three terms in G. P is 125/8, find G. M ? 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 The product of three terms in G. P is 125/8, find G. M ? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The product of three terms in G. P is 125/8, find G. M ?.
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