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The sum of the first two terms of a GP is 5/3 and the sum of infinity of the series is 3. The common ratio is?
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The sum of the first two terms of a GP is 5/3 and the sum of infinity ...
Given:
- The sum of the first two terms of a GP is 5/3
- The sum of infinity of the series is 3
To find:
The common ratio (r)
Solution:
Step 1: Find the first two terms of the GP
Let the first term be a and the common ratio be r
Therefore, the second term will be ar
Given, the sum of the first two terms of the GP is 5/3
Therefore, a + ar = 5/3
=> a(1 + r) = 5/3
=> a = 5/3(1 + r)^-1
Step 2: Find the sum to infinity of the GP
The sum to infinity of a GP is given by S = a/(1 - r)
Given, the sum of infinity of the series is 3
Therefore, a/(1 - r) = 3
Substituting the value of a from step 1, we get:
5/3(1 + r)^-1 / (1 - r) = 3
=> 5/(3(1 + r)(1 - r)) = 3
=> 5 = 9(1 - r^2)
=> 5/9 = 1 - r^2
=> r^2 = 4/9
=> r = ±2/3
Step 3: Determine the value of r
The common ratio of a GP cannot be negative. Therefore, r = 2/3.
Answer:
The common ratio of the GP is 2/3.
- The sum of the first two terms of a GP is 5/3
- The sum of infinity of the series is 3
To find:
The common ratio (r)
Solution:
Step 1: Find the first two terms of the GP
Let the first term be a and the common ratio be r
Therefore, the second term will be ar
Given, the sum of the first two terms of the GP is 5/3
Therefore, a + ar = 5/3
=> a(1 + r) = 5/3
=> a = 5/3(1 + r)^-1
Step 2: Find the sum to infinity of the GP
The sum to infinity of a GP is given by S = a/(1 - r)
Given, the sum of infinity of the series is 3
Therefore, a/(1 - r) = 3
Substituting the value of a from step 1, we get:
5/3(1 + r)^-1 / (1 - r) = 3
=> 5/(3(1 + r)(1 - r)) = 3
=> 5 = 9(1 - r^2)
=> 5/9 = 1 - r^2
=> r^2 = 4/9
=> r = ±2/3
Step 3: Determine the value of r
The common ratio of a GP cannot be negative. Therefore, r = 2/3.
Answer:
The common ratio of the GP is 2/3.
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The sum of the first two terms of a GP is 5/3 and the sum of infinity of the series is 3. The common ratio is?
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The sum of the first two terms of a GP is 5/3 and the sum of infinity of the series is 3. 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 two terms of a GP is 5/3 and the sum of infinity of the series is 3. 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 two terms of a GP is 5/3 and the sum of infinity of the series is 3. The common ratio is?.
The sum of the first two terms of a GP is 5/3 and the sum of infinity of the series is 3. 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 two terms of a GP is 5/3 and the sum of infinity of the series is 3. 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 two terms of a GP is 5/3 and the sum of infinity of the series is 3. The common ratio is?.
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