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The sequence of numbers a1, a2, a3, , an, is defined by
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Updated on: 20 Jun 2024, 16:54
Updated on: 20 Jun 2024, 16:54
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75% (01:42) correct
24% (01:51) wrong based on 107 sessions
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The sequence of numbers a1, a2, a3, …, an, … is defined by \(a_n=2^n - \frac{1}{2^{n-33}}\) for each integer n ≥ 1
Quantity A |
Quantity B |
The sum of the first 32 terms of this sequence |
The sum of the first 31 terms of this sequence |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The sequence of numbers a1, a2, a3, , an, is defined by
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21 Sep 2017, 07:55
21 Sep 2017, 07:55
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Since until the 31st term the two sums are equal we can focus on the 32nd term, which is equal to \(2^{32}-\frac{1}{2^{32-33}}=2^{32}-\frac{1}{2^{-1}}=2^{32}-2>0\). Thus quantity A is larger!
Re: The sequence of numbers a1, a2, a3, , an, is defined by
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22 Feb 2018, 06:48
22 Feb 2018, 06:48
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With a little concern, we can find out the answer. Since 31st terms of both sides are equal, we can eliminate them. Then by calculating, we can see that the quantity A is bigger than the quantity B.
