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The sequence
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22 Sep 2021, 02:43
22 Sep 2021, 02:43
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The sequence \(a_1,a_2,a_3,…a_n\),… is such that \(a_1=−2,a_2=−5,a_3=4,a_4=3\),and \(a_n=a_{n−4}\) for \(n>4\).
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.
Source: manhattanreview
Quantity A |
Quantity B |
The sum of the first 64 terms of the sequence |
The sum of the first 98 terms of the sequence |
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.
Source: manhattanreview
Re: The sequence
[#permalink]
24 Sep 2021, 10:50
24 Sep 2021, 10:50
1
Carcass wrote:
The sequence \(a_1,a_2,a_3,…a_n\),… is such that \(a_1=−2,a_2=−5,a_3=4,a_4=3\),and \(a_n=a_{n−4}\) for \(n>4\).
Quantity A |
Quantity B |
The sum of the first 64 terms of the sequence |
The sum of the first 98 terms of the sequence |
Since \(a_n=a_{n−4}\), the values will repeat every 4 numbers as -2,-5,4,3,-2,-5,4,3,-2,-5,4,3,-2,-5,4,3,...
For sum of first 64, find the sum of 4 and multiply by 16 : (-2 -5 + 4 +3) * 16 = 0 * 16 = 0
For sum of first 98, 98 is not a multiple of 4, the reminder of 98/4 is 2, so sum of first 98 will be -2 -5 = -7.
Quantity A is greater.
Re: The sequence
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16 Dec 2025, 08:36
16 Dec 2025, 08:36
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