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 a certain sequence, the term an is defined by the formula
[#permalink]
27 Jul 2018, 07:17
27 Jul 2018, 07:17
Expert Reply
3
Bookmarks
00:00
Question Stats:
64% (02:32) correct
35% (02:47) wrong based on 78 sessions
Hide Show timer Statistics
In a certain sequence, the term an is defined by the formula \(a_n = 2 \times a_{n - 1}\) for each integer n ≥ 2. If \(a_1 = 1\), what is the positive difference between the sum of the first 10 terms of the sequence and the sum of the 11th and 12th terms of the same sequence?
(A) 1
(B) 1,024
(C) 1,025
(D) 2,048
(E) 2,049
(A) 1
(B) 1,024
(C) 1,025
(D) 2,048
(E) 2,049
Re: In a certain sequence, the term an is defined by the formula
[#permalink]
12 Aug 2018, 05:35
12 Aug 2018, 05:35
Expert Reply
1
Bookmarks
Explanation
This is a geometric sequence: each new number is created by multiplying the previous number by 2.
Calculate the first few terms of the series to find the pattern: 1, 2, 4, 8, 16, and so on.
Geometric sequences can be written in this form: \(a_n = r^{n – 1}\), where r is the multiplied constant and n is the number of the desired term. In this case, the function is \(a_n = 2^{n – 1}\).
The question asks for the difference between the sum of the first 10 terms and the sum of the 11th and 12th terms. While there is a clever pattern at play, it is hard to spot. If you don’t see the pattern, one way to solve is to use the calculator to add the first ten terms: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1,023.
The 11th term plus the 12th term is equal to 1,024 + 2,048 = 3,072. Subtract 1,023 to get 2,049.
This is a geometric sequence: each new number is created by multiplying the previous number by 2.
Calculate the first few terms of the series to find the pattern: 1, 2, 4, 8, 16, and so on.
Geometric sequences can be written in this form: \(a_n = r^{n – 1}\), where r is the multiplied constant and n is the number of the desired term. In this case, the function is \(a_n = 2^{n – 1}\).
The question asks for the difference between the sum of the first 10 terms and the sum of the 11th and 12th terms. While there is a clever pattern at play, it is hard to spot. If you don’t see the pattern, one way to solve is to use the calculator to add the first ten terms: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 = 1,023.
The 11th term plus the 12th term is equal to 1,024 + 2,048 = 3,072. Subtract 1,023 to get 2,049.
Re: In a certain sequence, the term an is defined by the formula
[#permalink]
19 Jul 2020, 12:05
19 Jul 2020, 12:05
Does GRE bring something like that ?
