GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
In the sequence of numbers a_1,a_2,a_3
[#permalink]
14 May 2020, 13:52
14 May 2020, 13:52
1
Expert Reply
7
Bookmarks
00:00
Question Stats:
62% (01:36) correct
37% (01:20) wrong based on 208 sessions
Hide Show timer Statistics
In the sequence of numbers \(a_1,a_2,a_3....,a_n......\)is defined by \(a_n=2^n -\frac{1}{2^{n-21}}\) for each integer \(n \neq 1\)
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.
Quantity A |
Quantity B |
The sum of the first 20 terms of this sequence |
The sum of the first 19 terms of this 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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the sequence of numbers a_1,a_2,a_3
[#permalink]
15 May 2020, 05:59
15 May 2020, 05:59
3
2
Bookmarks
Carcass wrote:
In the sequence of numbers \(a_1,a_2,a_3....,a_n......\)is defined by \(a_n=2^n -\frac{1}{2^{n-21}}\) for each integer \(n \neq 1\)
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.
Quantity A |
Quantity B |
The sum of the first 20 terms of this sequence |
The sum of the first 19 terms of this 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.
We have:
Quantity A: \(a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19}+ a_{20}\)
Quantity B: \(a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19}\)
Subtract \((a_1 + a_2 + a_3 + ....+ a_{18}+ a_{19})\) from both quantities to get:
Quantity A: \(a_{20}\)
Quantity B: \(0\)
GIVEN: \(a_n=2^n -\frac{1}{2^{n-21}}\)
So, \(a_{20}=2^{20} -\frac{1}{2^{20-21}}=2^{20} -\frac{1}{2^{-1}}=2^{20} - 2^{1} =\) (a very very big number) - 2
We get:
Quantity A: (a very very big number) - 2
Quantity B: 0
Answer: A
Cheers,
Brent
General Discussion
Re: In the sequence of numbers a_1,a_2,a_3
[#permalink]
20 Jun 2020, 22:52
20 Jun 2020, 22:52
Hello,
What do you mean by n # 1. for n=1 dont we have : 2-2^20?
What do you mean by n # 1. for n=1 dont we have : 2-2^20?
