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The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP is
- a)>1
- b)Independent of first term of AP
- c)Independent of first term of GP
- d)< 1
Correct answer is option 'C'. Can you explain this answer?
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The first term of an AP = the common ratio of a GP and the first term ...
This is independent of the first term of GP.
Most Upvoted Answer
The first term of an AP = the common ratio of a GP and the first term ...
2
b) 1/2
c) 1/3
d) 3
Let the first term of the AP be a and the common difference be d. Then, the second term of the AP is a + d.
Let the first term of the GP be r. Then, the second term of the GP is r^2.
Given that the sum of the first two terms of the GP is equal to the sum of the first two terms of the AP:
r + r^2 = a + (a + d)
r^2 + r - 2a - d = 0
Also, given that the first term of the AP = the common ratio of the GP and the first term of the GP = common difference of the AP:
a = r
d = r
Substituting these values in the equation above:
r^2 + r - 4r = 0
r(r - 3) = 0
Therefore, r = 0 or r = 3. Since the first term of the GP cannot be 0, we have r = 3.
Thus, the first term of the GP is 3 and the first term of the AP is also 3.
The ratio of the first term of the GP to the first term of the AP is:
3/3 = 1
Therefore, the answer is not given in the options.
b) 1/2
c) 1/3
d) 3
Let the first term of the AP be a and the common difference be d. Then, the second term of the AP is a + d.
Let the first term of the GP be r. Then, the second term of the GP is r^2.
Given that the sum of the first two terms of the GP is equal to the sum of the first two terms of the AP:
r + r^2 = a + (a + d)
r^2 + r - 2a - d = 0
Also, given that the first term of the AP = the common ratio of the GP and the first term of the GP = common difference of the AP:
a = r
d = r
Substituting these values in the equation above:
r^2 + r - 4r = 0
r(r - 3) = 0
Therefore, r = 0 or r = 3. Since the first term of the GP cannot be 0, we have r = 3.
Thus, the first term of the GP is 3 and the first term of the AP is also 3.
The ratio of the first term of the GP to the first term of the AP is:
3/3 = 1
Therefore, the answer is not given in the options.
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The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer?
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The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer?.
The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The first term of an AP = the common ratio of a GP and the first term of the GP = common difference of the AP. If the sum of the first two terms of the GP is equal to the sum of the first 2 terms of the AP, then the ratio of the first term of the GP to the first term of an AP isa)>1b)Independent of first term of APc)Independent of first term of GPd)< 1Correct answer is option 'C'. Can you explain this answer?.
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