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 sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for
[#permalink]
25 Jul 2018, 17:25
25 Jul 2018, 17:25
Expert Reply
1
Bookmarks
00:00
Question Stats:
94% (01:53) correct
5% (02:04) wrong based on 52 sessions
Hide Show timer Statistics
The sequence S is defined by \(S_n = S_{n – 1} + S_{n – 2} – 3\) for each integer n ≥ 3. If \(S_1 = 5\) and \(S_2 = 0\), what is the value of \(S_6\)?
(A) –6
(B) –5
(C) –3
(D) –1
(E) 1
(A) –6
(B) –5
(C) –3
(D) –1
(E) 1
Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for
[#permalink]
11 Aug 2018, 16:54
11 Aug 2018, 16:54
Expert Reply
Explanation
The sequence \(S_n = S_{n – 1} + S_{n - 2} - 3\) can be read as “to get any term in sequence S, sum the two previous terms and subtract 3.”
The problem gives the first two terms and asks for the sixth term:
To get any term, sum the two previous terms and subtract 3. So the third term will equal 5 + 0 – 3 = 2.
The fourth term will equal 0 + 2 – 3 = –1. The fifth term will equal 2 + (–1) – 3 = –2. The sixth term will equal –1 + (–2) – 3 = –6:
The sequence \(S_n = S_{n – 1} + S_{n - 2} - 3\) can be read as “to get any term in sequence S, sum the two previous terms and subtract 3.”
The problem gives the first two terms and asks for the sixth term:
| 5 | 0 | ||||
| \(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) | \(S_6\) |
To get any term, sum the two previous terms and subtract 3. So the third term will equal 5 + 0 – 3 = 2.
The fourth term will equal 0 + 2 – 3 = –1. The fifth term will equal 2 + (–1) – 3 = –2. The sixth term will equal –1 + (–2) – 3 = –6:
| 5 | 0 | 2 | -1 | -2 | -6 |
| \(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) | \(S_6\) |
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1111
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Re: The sequence S is defined by Sn = Sn 1 + Sn 2 3 for
[#permalink]
20 Sep 2022, 08:40
20 Sep 2022, 08:40
1
Given that \(S_n = S_{n - 1} + S_{n - 2} - 3\), \(S_1 = 5\) and \(S_2 = 0\) and we need to find the value of \(S_6\)
\(S_3 = S_{3 - 1} + S_{3 - 2} - 3\) = \(S_{2} + S_{1} - 3\) = Sum of previous two terms - 3 = 0 + 5 - 3 = 2
\(S_4\) = \(S_3\) + \(S_2\) - 3 = 2 + 0 - 3 = -1
\(S_5\) = \(S_4\) + \(S_3\) - 3 = -1 + 2 - 3 = -2
\(S_6\) = \(S_5\) + \(S_4\) - 3 = -2 + -1 - 3 = -6
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Sequence problems
\(S_3 = S_{3 - 1} + S_{3 - 2} - 3\) = \(S_{2} + S_{1} - 3\) = Sum of previous two terms - 3 = 0 + 5 - 3 = 2
\(S_4\) = \(S_3\) + \(S_2\) - 3 = 2 + 0 - 3 = -1
\(S_5\) = \(S_4\) + \(S_3\) - 3 = -1 + 2 - 3 = -2
\(S_6\) = \(S_5\) + \(S_4\) - 3 = -2 + -1 - 3 = -6
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Sequence problems
