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![A sequence S is defined as follows: S_{n}=[S_{n}+1+S_{n}-1]/2. If S_{1](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "A sequence S is defined as follows: S_{n}=[S_{n}+1+S_{n}-1]/2. If S_{1"){kind=icon}
13 Dec 2024, 12:17
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A sequence S is defined as follows: \(S_{n}=\frac{S_{n+1 } +S_{n-1 }}{2}\). If \(S_{1} = 15\) and \(S_{4} = 10.5\), what is \(S_{2}?\)
14 Dec 2024, 23:59
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Hi
Please see the solution in the file attached herewith.
The answer is 13.5.
Cheers!
Please see the solution in the file attached herewith.
The answer is 13.5.
Cheers!
Attachments
File comment: Solution to the question
151224.png [ 15.76 KiB | Viewed 289 times ]
27 Feb 2025, 10:24
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The easiest way to solve this problem is to write equations for \(S_{2}\) and \(S_{3}\) in terms of the other items in the sequence and solve for \(S_{2}:\)
Now substitute the expression for \(S_{3}\) into the first equation and solve:
GMAT-Club-Forum-uo7j1woa.png [ 76.36 KiB | Viewed 164 times ]
GMAT-Club-Forum-8h4gv34j.png [ 74.7 KiB | Viewed 164 times ]
The easiest way to solve this problem is to write equations for \(S_{2}\) and \(S_{3}\) in terms of the other items in the sequence and solve for \(S_{2}:\)
Now substitute the expression for \(S_{3}\) into the first equation and solve:
Attachment:
GMAT-Club-Forum-uo7j1woa.png [ 76.36 KiB | Viewed 164 times ]
Attachment:
GMAT-Club-Forum-8h4gv34j.png [ 74.7 KiB | Viewed 164 times ]
