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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
S_n represents the sum of the first n terms of sequence
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21 Jul 2022, 06:46
21 Jul 2022, 06:46
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Question Stats:
44% (02:42) correct
55% (02:04) wrong based on 9 sessions
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\(S_n\) represents the sum of the first \(n\) terms of sequence X. If \(S_n = n^2 – 6n + 9\), what is the value of 13th term of sequence X?
(A) -80
(B) 100/13
(C) 19
(D) 81
(E) 100
(A) -80
(B) 100/13
(C) 19
(D) 81
(E) 100
Re: S_n represents the sum of the first n terms of sequence
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22 Jul 2022, 05:11
22 Jul 2022, 05:11
explain please?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
S_n represents the sum of the first n terms of sequence
[#permalink]
22 Jul 2022, 05:52
22 Jul 2022, 05:52
2
GreenlightTestPrep wrote:
\(S_n\) represents the sum of the first \(n\) terms of sequence X. If \(S_n = n^2 – 6n + 9\), what is the value of 13th term of sequence X?
(A) -80
(B) 100/13
(C) 19
(D) 81
(E) 100
(A) -80
(B) 100/13
(C) 19
(D) 81
(E) 100
Notice that \(S_13 = term_1 + term_2 + term_3 + . . . term_{12} + term_{13}\)
And \(S_{12} = term_1 + term_2 + term_3 + . . . term_{11} + term_{12}\)
So, \(S_{13}\) \(-\) \(S_{12}\) \(= term_{13} \)
\(S_{13} = 13^2 – 6(13) + 9 = 100\)
\(S_{12}= 12^2 – 6(12) + 9 = 81\)
Aside: By recognizing x² – 6x + 9 = (x-3)², I could have saved myself a little bit of time calculating each sum
So, \(term_{13} = 100 - 81 = 19\)
Answer: C
