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A sequence contains the terms S_1
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16 May 2024, 01:32
16 May 2024, 01:32
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Question Stats:
87% (02:36) correct
12% (01:57) wrong based on 8 sessions
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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
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A sequence contains the terms S_1
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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
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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!
