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25 Sep 2018, 03:42
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
72% (01:53) correct
28%
(02:13)
wrong
based on 186
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[Math Revolution GMAT math practice question]
The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n?
\(A. n\)
\(B. n^2\)
\(C. –n\)
\(D. -n^2\)
\(E. (n-1)^2\)
The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n?
\(A. n\)
\(B. n^2\)
\(C. –n\)
\(D. -n^2\)
\(E. (n-1)^2\)
25 Sep 2018, 04:09
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We see that the increment in the given sequence is:
From S1 to S2: +1 = 1^2
From S2 to S3: +4 = 2^2
From S3 to S4: +9 = 3^2
From S4 to S5: +16 = 4^2
...
Thus from Sn-1 to Sn = (n-1)^2.
Answer E
From S1 to S2: +1 = 1^2
From S2 to S3: +4 = 2^2
From S3 to S4: +9 = 3^2
From S4 to S5: +16 = 4^2
...
Thus from Sn-1 to Sn = (n-1)^2.
Answer E
25 Sep 2018, 05:30
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MathRevolution
To answer any question of sequences, one needs to find a pattern so we keep looking at what we get when we canculate expressions like \(S_n - S_{n-1}\)
\(S_1 = 1\)
\(S_2 = 2\) i.e. \(S_2 - S_{1} = 1= 1^1\)
\(S_3 = 6\) i.e. \(S_3 - S_{2} = 4 = 2^2\)
\(S_4 = 15\) i.e. \(S_4 - S_{3} = 9 = 3^2\)
i.e. \(S_n - S_{n-1} = (n-1)^2\)
Answer: Option E
