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The infinite G.P. series with first term 1/4 and sum 1/3 is
- a)1/4, 1/16, 1/64….
- b)1/4, -1/16, 1/64..
- c)1/4, 1/8, 1/16…
- d)None
Correct answer is option 'A'. Can you explain this answer?
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The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16...
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The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16...
The formula for the sum of an infinite geometric series is:
S = a / (1 - r)
Where:
S = sum of the series
a = first term
r = common ratio
In this case, the first term (a) is 1/4 and the sum (S) is 1/3.
1/3 = (1/4) / (1 - r)
To solve for r, we can rearrange the equation:
1 - r = (1/4) / (1/3)
1 - r = (1/4) * (3/1)
1 - r = 3/4
r = 1 - (3/4)
r = 1/4
So the common ratio (r) is 1/4.
Now we can find the terms of the series by multiplying the first term (1/4) by the common ratio (1/4) repeatedly:
Term 1: 1/4
Term 2: (1/4) * (1/4) = 1/16
Term 3: (1/16) * (1/4) = 1/64
...
Therefore, the terms of the infinite geometric series are: 1/4, 1/16, 1/64, ...
S = a / (1 - r)
Where:
S = sum of the series
a = first term
r = common ratio
In this case, the first term (a) is 1/4 and the sum (S) is 1/3.
1/3 = (1/4) / (1 - r)
To solve for r, we can rearrange the equation:
1 - r = (1/4) / (1/3)
1 - r = (1/4) * (3/1)
1 - r = 3/4
r = 1 - (3/4)
r = 1/4
So the common ratio (r) is 1/4.
Now we can find the terms of the series by multiplying the first term (1/4) by the common ratio (1/4) repeatedly:
Term 1: 1/4
Term 2: (1/4) * (1/4) = 1/16
Term 3: (1/16) * (1/4) = 1/64
...
Therefore, the terms of the infinite geometric series are: 1/4, 1/16, 1/64, ...
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The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. Can you explain this answer?
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The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. 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 The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. 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 The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. Can you explain this answer?.
The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. 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 The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. 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 The infinite G.P. series with first term 1/4 and sum 1/3 isa)1/4, 1/16, 1/64….b)1/4, -1/16, 1/64..c)1/4, 1/8, 1/16…d)NoneCorrect answer is option 'A'. Can you explain this answer?.
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