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.
The general term for a sequence is given as
[#permalink]
13 May 2024, 23:56
13 May 2024, 23:56
Expert Reply
1
Bookmarks
00:00
Question Stats:
88% (03:08) correct
11% (03:04) wrong based on 17 sessions
Hide Show timer Statistics
The general term for a sequence is given as \(a_n=a_{(n-1)} -a_{(n-2)}\). If \(a_1=-5\) and \(a_2=4\). What is the sum of the first 100 terms?
A. 10
B. 11
C. 12
D. 13
E. 14
A. 10
B. 11
C. 12
D. 13
E. 14
Part of the project: GRE Quant & Verbal ADVANCED Daily Challenge 2024 Edition - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
Manager
Joined: 11 Nov 2023
Posts: 228
Given Kudos: 78
WE:Business Development (Advertising and PR)
The general term for a sequence is given as
[#permalink]
15 May 2024, 10:36
15 May 2024, 10:36
3
1
Bookmarks
Calculate some terms to identify a pattern.
\(a_3 = a_{(3-1)} - a_{(3-2)} = a_2 - a_1 = 4 - (-5) = 9 \)
\(a_4 = a_3 - a_2 = 9 - 4 = 5 \)
\(a_5 = a_4 - a_3 = 5 - 9 = -4 \)
\(a_6 = a_5 - a_4 = -4 - 5 = -9 \)
\(a_7 = a_6 - a_5 = -9 - (-4) = -5 \)
The first 6 terms are -5, 4, 9, 5, -4, -9 and its sum is 0. The pattern "resets" on the 7th term, i.e., equals the 1st term.
Thus, the sum of terms that are multiples of 6 is 0. I.e., the sum of the first 96 terms is also 0.
That leaves terms 97, 98, 99, and 100, which will be -5, 4, 9, and 5.
The sum of those 4 terms = -5 + 4 + 9 + 5 = 13
\(a_3 = a_{(3-1)} - a_{(3-2)} = a_2 - a_1 = 4 - (-5) = 9 \)
\(a_4 = a_3 - a_2 = 9 - 4 = 5 \)
\(a_5 = a_4 - a_3 = 5 - 9 = -4 \)
\(a_6 = a_5 - a_4 = -4 - 5 = -9 \)
\(a_7 = a_6 - a_5 = -9 - (-4) = -5 \)
The first 6 terms are -5, 4, 9, 5, -4, -9 and its sum is 0. The pattern "resets" on the 7th term, i.e., equals the 1st term.
Thus, the sum of terms that are multiples of 6 is 0. I.e., the sum of the first 96 terms is also 0.
That leaves terms 97, 98, 99, and 100, which will be -5, 4, 9, and 5.
The sum of those 4 terms = -5 + 4 + 9 + 5 = 13
Re: The general term for a sequence is given as
[#permalink]
19 May 2024, 05:16
19 May 2024, 05:16
1
nurirachel wrote:
Calculate some terms to identify a pattern.
\(a_3 = a_{(3-1)} - a_{(3-2)} = a_2 - a_1 = 4 - (-5) = 9 \)
\(a_4 = a_3 - a_2 = 9 - 4 = 5 \)
\(a_5 = a_4 - a_3 = 5 - 9 = -4 \)
\(a_6 = a_5 - a_4 = -4 - 5 = -9 \)
\(a_7 = a_6 - a_5 = -9 - (-4) = -5 \)
The first 6 terms are -5, 4, 9, 5, -4, -9 and its sum is 0. The pattern "resets" on the 7th term, i.e., equals the 1st term.
Thus, the sum of terms that are multiples of 6 is 0. I.e., the sum of the first 96 terms is also 0.
That leaves terms 97, 98, 99, and 100, which will be -5, 4, 9, and 5.
The sum of those 4 terms = -5 + 4 + 9 + 5 = 13
\(a_3 = a_{(3-1)} - a_{(3-2)} = a_2 - a_1 = 4 - (-5) = 9 \)
\(a_4 = a_3 - a_2 = 9 - 4 = 5 \)
\(a_5 = a_4 - a_3 = 5 - 9 = -4 \)
\(a_6 = a_5 - a_4 = -4 - 5 = -9 \)
\(a_7 = a_6 - a_5 = -9 - (-4) = -5 \)
The first 6 terms are -5, 4, 9, 5, -4, -9 and its sum is 0. The pattern "resets" on the 7th term, i.e., equals the 1st term.
Thus, the sum of terms that are multiples of 6 is 0. I.e., the sum of the first 96 terms is also 0.
That leaves terms 97, 98, 99, and 100, which will be -5, 4, 9, and 5.
The sum of those 4 terms = -5 + 4 + 9 + 5 = 13
I would add that this is a recursive sequence. Sequences that follow patterns like that in the question stem should immediately make students think about iterative calculations to find a pattern.
While that's not in itself a formula, it's a great example of the GRE test makers giving students a clue to quickly find a solution.
