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a1,a2,a3,....an,...
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25 Dec 2019, 02:33
25 Dec 2019, 02:33
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\(a_1,a_2,a_3,....a_n,...\)
In the sequence above, \(a_1=1\) and for each term after the first term, \(a_n=(\frac{1}{2})a_{n - 1}\)
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 right answer and explanation
In the sequence above, \(a_1=1\) and for each term after the first term, \(a_n=(\frac{1}{2})a_{n - 1}\)
Quantity A |
Quantity B |
\(a_{11}\) |
\(0.001\) |
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 right answer and explanation
Re: a1,a2,a3,....an,...
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03 Jan 2020, 20:28
03 Jan 2020, 20:28
2
By Sequence a1=1, a2=1/2, a3 = 1/(2)^2
since a1=1
a11 = 1/(2)^10 = 1/1024 = A
B =0.001 = 1/1000
The numerator is the same for both A and B (both positive numbers), But denominator is high is A so the value of A is less.
Hence, B is the greater of two and it is the answer.
since a1=1
a11 = 1/(2)^10 = 1/1024 = A
B =0.001 = 1/1000
The numerator is the same for both A and B (both positive numbers), But denominator is high is A so the value of A is less.
Hence, B is the greater of two and it is the answer.
Re: a1,a2,a3,....an,...
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31 May 2020, 18:07
31 May 2020, 18:07
2
Any time that you can turn a sequence into a straight up function, go do that as long as it's easy enough.
In this case, write out the first few terms...
1st term: 1
2nd term: 1/2
3rd term: 1/4
4th term: 1/8
This sequence's "nth" value can be denoted by (1/2)^(n-1)
So the 11th value is: (1/2)^(11-1) = (1/2)^(10)
Which is equivalent to 1/(2^10) = 1/(2^4*2^4*4) = 1/1024
You should know immediately that that is less than B; therefore, answer is B!
In this case, write out the first few terms...
1st term: 1
2nd term: 1/2
3rd term: 1/4
4th term: 1/8
This sequence's "nth" value can be denoted by (1/2)^(n-1)
So the 11th value is: (1/2)^(11-1) = (1/2)^(10)
Which is equivalent to 1/(2^10) = 1/(2^4*2^4*4) = 1/1024
You should know immediately that that is less than B; therefore, answer is B!
