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Sequence S is such that Sn
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02 Mar 2018, 03:32
02 Mar 2018, 03:32
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Question Stats:
70% (02:09) correct
29% (02:29) wrong based on 112 sessions
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Sequence S is such that \(S_n = S_{n-1} + \frac{3}{2}\) and \(S_1 = 2\)
Sequence A is such that \(A_n = A_{n-1} - 1.5\) and \(A_1 = 18.5\)
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Kudos for the correct answer AND explanation
Sequence A is such that \(A_n = A_{n-1} - 1.5\) and \(A_1 = 18.5\)
Quantity A |
Quantity B |
The sum of the terms in \(S\) from \(S_1\) to \(S_{13}\), inclusive |
The sum of the terms from in \(A\) from \(A_1\) to \(A_{13}\), inclusive |
A. The quantity in Column A is greater
B. The quantity in Column B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Kudos for the correct answer AND explanation
Re: Sequence S is such that Sn
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02 Mar 2018, 10:03
02 Mar 2018, 10:03
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Formula given to us:
\(Sn = Sn-1 +1.5; s1 = 2 and
An = An-1 - 1.5; A1 = 18.5\)
For the first sequence
Each subsequent value of \(s\) is greater by \(1.5\) For solving the question we need to calculate the sum of first 13 terms
we have the 1st term as \(2\). There remains \(12\) more terms. We know that there is an increase of \(1.5\) per term hence there is a total increase of \(12 * 1.5 = 18\)
Last term of the sequence = \(2+18 = 20\)
Since the sequence is equally spaced avg = \(\frac{2 +20}{2} = 11\)
There are a total of \(13\) terms hence sum of the sequence = \(11* 13 = 143\)
For the second sequence
Each subsequent value of A is less by \(1.5\) For solving the question we need to calculate the sum of first \(13\) terms
we have the 1st term as \(18.5\) There remains \(12\) more terms. We know that there is a decrease of \(1.5\) per term hence there is a total decrease of \(12 * 1.5 = 18\)
Last term of the sequence = \(18.5 - 18 = 0.5\)
Since the sequence is equally spaced avg = \(\frac{0.5 +18.5}{2} = 9.5\)
There are a total of \(13\) terms hence sum of the sequence = \(9.5* 13 = 123.5\)
Option A
\(Sn = Sn-1 +1.5; s1 = 2 and
An = An-1 - 1.5; A1 = 18.5\)
For the first sequence
Each subsequent value of \(s\) is greater by \(1.5\) For solving the question we need to calculate the sum of first 13 terms
we have the 1st term as \(2\). There remains \(12\) more terms. We know that there is an increase of \(1.5\) per term hence there is a total increase of \(12 * 1.5 = 18\)
Last term of the sequence = \(2+18 = 20\)
Since the sequence is equally spaced avg = \(\frac{2 +20}{2} = 11\)
There are a total of \(13\) terms hence sum of the sequence = \(11* 13 = 143\)
For the second sequence
Each subsequent value of A is less by \(1.5\) For solving the question we need to calculate the sum of first \(13\) terms
we have the 1st term as \(18.5\) There remains \(12\) more terms. We know that there is a decrease of \(1.5\) per term hence there is a total decrease of \(12 * 1.5 = 18\)
Last term of the sequence = \(18.5 - 18 = 0.5\)
Since the sequence is equally spaced avg = \(\frac{0.5 +18.5}{2} = 9.5\)
There are a total of \(13\) terms hence sum of the sequence = \(9.5* 13 = 123.5\)
Option A
