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.
A sequence contains the terms S_1
[#permalink]
16 May 2024, 01:32
16 May 2024, 01:32
Expert Reply
00:00
Question Stats:
83% (02:17) correct
16% (02:00) wrong based on 12 sessions
Hide Show timer Statistics
A sequence contains the terms \(S_1, S_2,S_3................S_n\) where \(S_2=2\) and \(S_n=S_{(n-1)}+2S_2\) . What is the value of \(S_{18}\) ?
A. 60
B. 63
C. 66
D. 70
E. 75
A. 60
B. 63
C. 66
D. 70
E. 75
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)
A sequence contains the terms S_1
[#permalink]
16 May 2024, 08:36
16 May 2024, 08:36
1
Calculate the first few terms of the sequence to identify a pattern.
\(S_3 = S_{(3-1)}+2S_2 = S_2 + 2S_2 = 2 + 2(2) = 6 \)
\(S_4 = S_{(4-1)}+2S_2 = S_3 + 2S_2 = [2 + 2(2)] + 2(2) = 10 \)
\(S_5 = S_{(5-1)}+2S_2 = S_4 + 2S_2 = [2 + 2(2) + 2(2)] + 2(2) = 14 \)
We can see that \(S_n\) can also be written as \(2 + 4(n-2)\).
\(S_{18} = 2 + 4(18-2) = 2 + 4(16) = 2 + 64 = 66\)
\(S_3 = S_{(3-1)}+2S_2 = S_2 + 2S_2 = 2 + 2(2) = 6 \)
\(S_4 = S_{(4-1)}+2S_2 = S_3 + 2S_2 = [2 + 2(2)] + 2(2) = 10 \)
\(S_5 = S_{(5-1)}+2S_2 = S_4 + 2S_2 = [2 + 2(2) + 2(2)] + 2(2) = 14 \)
We can see that \(S_n\) can also be written as \(2 + 4(n-2)\).
\(S_{18} = 2 + 4(18-2) = 2 + 4(16) = 2 + 64 = 66\)
A sequence contains the terms S_1
[#permalink]
17 May 2024, 16:12
17 May 2024, 16:12
1
If you knew the formula for finding the nth term in a sequence, you could solve this question in 45-60 seconds.
Given the recursive sequence Sn = Sn−1+4 starting from S2 = 2, we recognise that this is an arithmetic sequence with the first term S2 and common difference 4. Just to illustrate this...
S2 = S(2-1)+4
OR
S2 = S1 + 4
The formula for the nth term in a sequence is: Sn = S2+(n−2)(d)
Plug in the numbers and you can quickly solve for S18...
Here, the common difference, d, equals 4, and S2 = 2 and n equals 18 (the 18th term in the sequence)
S18 = 2 + (18-2)(4)
S18 = 2 + (16)(4)
S18 = 2 + 64 = 66
There is a great chapter on arithmetic and geometric sequences in the Ultimate GRE Cheat Sheet. You will see some AWESOME time saving techniques in there. Check it out at Ultimate Tuition!
Given the recursive sequence Sn = Sn−1+4 starting from S2 = 2, we recognise that this is an arithmetic sequence with the first term S2 and common difference 4. Just to illustrate this...
S2 = S(2-1)+4
OR
S2 = S1 + 4
The formula for the nth term in a sequence is: Sn = S2+(n−2)(d)
Plug in the numbers and you can quickly solve for S18...
Here, the common difference, d, equals 4, and S2 = 2 and n equals 18 (the 18th term in the sequence)
S18 = 2 + (18-2)(4)
S18 = 2 + (16)(4)
S18 = 2 + 64 = 66
There is a great chapter on arithmetic and geometric sequences in the Ultimate GRE Cheat Sheet. You will see some AWESOME time saving techniques in there. Check it out at Ultimate Tuition!
