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If an infinite GP has the first term x and the sum 5, then which of the following is correct?
- a)x < –10
- b)–10 < x < 0
- c)0 < x < 10
- d)x > 10
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If an infinite GP has the first term x and the sum 5, then which of th...
Infinite GP sum formula = ar + ar² + ar³ + .........
Where a is the first term and r is the common ratio
If |r| < 1, the sum converges
If |r| > 1, the sum doesn't exist and series diverges.
Given:
First term = a = x
Hence from the equation of |r| < 1
where |r| < 1
Thus, 0 < x < 10.
Where a is the first term and r is the common ratio
If |r| < 1, the sum converges
If |r| > 1, the sum doesn't exist and series diverges.
Given:
First term = a = x
Hence from the equation of |r| < 1
where |r| < 1
Thus, 0 < x < 10.
Most Upvoted Answer
If an infinite GP has the first term x and the sum 5, then which of th...
The formula for the sum of an infinite geometric series is:
S = a/(1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this case, we are given that the first term is x and the sum is 5. So we can set up the equation:
5 = x/(1 - r)
To solve for x or r, we need another equation. One possibility is the formula for the nth term of a geometric series:
an = ar^(n-1)
where an is the nth term, a is the first term, and r is the common ratio.
We can use this formula to find an expression for x in terms of r:
x = a = a1 = ar^0 = 1
Substituting this into the first equation, we get:
5 = 1/(1 - r)
Solving for r, we get:
r = 4/5
So the common ratio is 4/5. We can also use this to find x:
x = a = a1 = 1
Therefore, the correct option is (d) x = 1.
S = a/(1 - r)
where S is the sum, a is the first term, and r is the common ratio.
In this case, we are given that the first term is x and the sum is 5. So we can set up the equation:
5 = x/(1 - r)
To solve for x or r, we need another equation. One possibility is the formula for the nth term of a geometric series:
an = ar^(n-1)
where an is the nth term, a is the first term, and r is the common ratio.
We can use this formula to find an expression for x in terms of r:
x = a = a1 = ar^0 = 1
Substituting this into the first equation, we get:
5 = 1/(1 - r)
Solving for r, we get:
r = 4/5
So the common ratio is 4/5. We can also use this to find x:
x = a = a1 = 1
Therefore, the correct option is (d) x = 1.
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If an infinite GP has the first term x and the sum 5, then which of the following is correct?a)x < –10b)–10 < x < 0c)0 < x < 10d)x > 10Correct answer is option 'C'. Can you explain this answer?
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If an infinite GP has the first term x and the sum 5, then which of the following is correct?a)x < –10b)–10 < x < 0c)0 < x < 10d)x > 10Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If an infinite GP has the first term x and the sum 5, then which of the following is correct?a)x < –10b)–10 < x < 0c)0 < x < 10d)x > 10Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If an infinite GP has the first term x and the sum 5, then which of the following is correct?a)x < –10b)–10 < x < 0c)0 < x < 10d)x > 10Correct answer is option 'C'. Can you explain this answer?.
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