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Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, then
- a)a = 7/4, r = 3/7
- b)a = 2, r = 3/8
- c)a = 3/2, r = 1/2
- d)a = 3, r = 1/4
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider an infinite series with first term 'a' and common rat...
To find the values of 'a' and 'r' for the given infinite series, we can use the formula for the sum of an infinite geometric series.
The formula for the sum of an infinite geometric series is given by:
S = a / (1 - r)
where S is the sum of the series, 'a' is the first term, and 'r' is the common ratio.
Given that the sum of the series is 4 and the second term is 3/4, we can substitute these values into the formula and solve for 'a' and 'r'.
Substituting S = 4, a = a, and r = r into the formula, we have:
4 = a / (1 - r)
We are also given that the second term is 3/4. The second term of a geometric series can be found using the formula:
T2 = a * r
Substituting a = a and r = r into the formula, we have:
3/4 = a * r
From the second equation, we can solve for 'r' in terms of 'a' by rearranging the equation:
r = (3/4) / a
Substituting this value of 'r' into the first equation, we have:
4 = a / (1 - (3/4) / a)
Simplifying this equation, we get:
4 = a / (1 - 3/4a)
Multiplying both sides of the equation by (1 - 3/4a), we have:
4(1 - 3/4a) = a
Expanding the equation, we get:
4 - 3/a = a
Rearranging the equation, we get:
a^2 - 4a + 3 = 0
Factoring the quadratic equation, we have:
(a - 3)(a - 1) = 0
This gives us two possible values for 'a': a = 3 or a = 1.
If we substitute a = 3 into the equation 3/4 = a * r, we can solve for 'r':
3/4 = 3 * r
r = 3/12
Simplifying, we get r = 1/4.
Therefore, the values of 'a' and 'r' for the given infinite series are a = 3 and r = 1/4, which matches option 'D'.
The formula for the sum of an infinite geometric series is given by:
S = a / (1 - r)
where S is the sum of the series, 'a' is the first term, and 'r' is the common ratio.
Given that the sum of the series is 4 and the second term is 3/4, we can substitute these values into the formula and solve for 'a' and 'r'.
Substituting S = 4, a = a, and r = r into the formula, we have:
4 = a / (1 - r)
We are also given that the second term is 3/4. The second term of a geometric series can be found using the formula:
T2 = a * r
Substituting a = a and r = r into the formula, we have:
3/4 = a * r
From the second equation, we can solve for 'r' in terms of 'a' by rearranging the equation:
r = (3/4) / a
Substituting this value of 'r' into the first equation, we have:
4 = a / (1 - (3/4) / a)
Simplifying this equation, we get:
4 = a / (1 - 3/4a)
Multiplying both sides of the equation by (1 - 3/4a), we have:
4(1 - 3/4a) = a
Expanding the equation, we get:
4 - 3/a = a
Rearranging the equation, we get:
a^2 - 4a + 3 = 0
Factoring the quadratic equation, we have:
(a - 3)(a - 1) = 0
This gives us two possible values for 'a': a = 3 or a = 1.
If we substitute a = 3 into the equation 3/4 = a * r, we can solve for 'r':
3/4 = 3 * r
r = 3/12
Simplifying, we get r = 1/4.
Therefore, the values of 'a' and 'r' for the given infinite series are a = 3 and r = 1/4, which matches option 'D'.
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Consider an infinite series with first term 'a' and common rat...
Consider gp a, ar, ar^2....Now ar=3/4 =>r=3/(4a)..........And sum of infinite term= a/(1-r)=4a/(1-{3/(4a)})=4=>16a-12=4a^2=>a^2-4a+3=0=> a=3 or a=1In options a=3 is given so this is correct (a=1 also correct since not given in option so d is correct)calculate r=3/4*3=1/4...
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Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer?
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Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer?.
Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer?.
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Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Consider an infinite series with first term 'a' and common ration 'r'. If it sum is 4 and the second term is 3/4, thena)a = 7/4, r = 3/7b)a = 2, r = 3/8c)a = 3/2, r = 1/2d)a = 3, r = 1/4Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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