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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
In a certain sequence, S_n represents the sum of all terms from
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14 Mar 2022, 03:00
14 Mar 2022, 03:00
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74% (01:56) correct
25% (02:00) wrong based on 27 sessions
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In a certain sequence, \(S_n\) represents the sum of all terms from \(t_1\) to \(t_n\), inclusive (for \(n ≥ 1\)).
If \(S_n = 3n^2\), what is the value of \(t_7\)?
A) 36
B) 39
C) 45
D) 49
E) 108
If \(S_n = 3n^2\), what is the value of \(t_7\)?
A) 36
B) 39
C) 45
D) 49
E) 108
Re: In a certain sequence, S_n represents the sum of all terms from
[#permalink]
14 Mar 2022, 10:31
14 Mar 2022, 10:31
1
GreenlightTestPrep wrote:
In a certain sequence, \(S_n\) represents the sum of all terms from \(t_1\) to \(t_n\), inclusive (for \(n ≥ 1\)).
If \(S_n = 3n^2\), what is the value of \(t_7\)?
A) 36
B) 39
C) 45
D) 49
E) 108
If \(S_n = 3n^2\), what is the value of \(t_7\)?
A) 36
B) 39
C) 45
D) 49
E) 108
t7 = S7 - S6
Lets calculate these values S7 = 3 * 7*7 = 147
S6 = 3 *6*6 = 108
So, t7 = 147 - 108 = 39 option B
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In a certain sequence, S_n represents the sum of all terms from
[#permalink]
14 Mar 2022, 11:31
14 Mar 2022, 11:31
GreenlightTestPrep wrote:
In a certain sequence, \(S_n\) represents the sum of all terms from \(t_1\) to \(t_n\), inclusive (for \(n ≥ 1\)).
If \(S_n = 3n^2\), what is the value of \(t_7\)?
A) 36
B) 39
C) 45
D) 49
E) 108
If \(S_n = 3n^2\), what is the value of \(t_7\)?
A) 36
B) 39
C) 45
D) 49
E) 108
First recognize that \(S_7 = t_1 + t_2 + t_3 + t_4 + t_5 + t_6 + t_7\), and \(S_6 = t_1 + t_2 + t_3 + t_4 + t_5 + t_6\)
This means, \(S_7 - S_6 = (t_1 + t_2 + t_3 + t_4 + t_5 + t_6 + t_7) - (t_1 + t_2 + t_3 + t_4 + t_5 + t_6) = t_7\) (which is exactly what we're trying to find the value of)
\(S_7 = 3(7)^2\), and \(S_6 = 3(6)^2\)
So, \(S_7 - S_6 = 3(7)^2 - 3(6)^2 = 39 = t_7\)
Answer: B
