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The sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is?
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Problem: The sum of the first 20 terms of a GP is 244 times the sum of its first 10 terms. Find the common ratio.
Solution:
Let the first term of the GP be 'a' and the common ratio be 'r'.
We know that the sum of the first 'n' terms of a GP is given by:
Sₙ = a(1 - rⁿ)/(1 - r)
Using this formula, we can find the sum of the first 20 terms and the sum of the first 10 terms:
S₂₀ = a(1 - r²⁰)/(1 - r)
S₁₀ = a(1 - r¹⁰)/(1 - r)
We are given that:
S₂₀ = 244S₁₀
Substituting the values of S₂₀ and S₁₀, we get:
a(1 - r²⁰)/(1 - r) = 244a(1 - r¹⁰)/(1 - r)
Cancelling out the common factor of 'a' from both sides, we get:
(1 - r²⁰)/(1 - r) = 244(1 - r¹⁰)/(1 - r)
Expanding the brackets and simplifying the equation, we get:
r¹⁰ = 1/244
Taking the 10th root of both sides, we get:
r = 1/2.44
Therefore, the common ratio is 0.4098 (approx).
Answer: The common ratio is 0.4098.
Solution:
Let the first term of the GP be 'a' and the common ratio be 'r'.
We know that the sum of the first 'n' terms of a GP is given by:
Sₙ = a(1 - rⁿ)/(1 - r)
Using this formula, we can find the sum of the first 20 terms and the sum of the first 10 terms:
S₂₀ = a(1 - r²⁰)/(1 - r)
S₁₀ = a(1 - r¹⁰)/(1 - r)
We are given that:
S₂₀ = 244S₁₀
Substituting the values of S₂₀ and S₁₀, we get:
a(1 - r²⁰)/(1 - r) = 244a(1 - r¹⁰)/(1 - r)
Cancelling out the common factor of 'a' from both sides, we get:
(1 - r²⁰)/(1 - r) = 244(1 - r¹⁰)/(1 - r)
Expanding the brackets and simplifying the equation, we get:
r¹⁰ = 1/244
Taking the 10th root of both sides, we get:
r = 1/2.44
Therefore, the common ratio is 0.4098 (approx).
Answer: The common ratio is 0.4098.
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The sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is?
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The sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is? 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 sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is?.
The sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is? 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 sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the first 20 term of a GP is 244 times the sum of its first 10term the common ratio is?.
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