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The sequence S is defined by Sn – 1 = (Sn) for each integer
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25 Jul 2018, 17:31
25 Jul 2018, 17:31
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Question Stats:
72% (01:07) correct
27% (01:08) wrong based on 122 sessions
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The sequence S is defined by \(S_{n – 1} = \frac{1}{4}(S_n)\) for each integer n ≥ 2. If \(S_1 = –4\), what is the value of \(S_4\)?
(A) –256
(B) –64
(C)\(\frac{-1}{16}\)
(D)\(\frac{1}{16}\)
(E) 256
(A) –256
(B) –64
(C)\(\frac{-1}{16}\)
(D)\(\frac{1}{16}\)
(E) 256
Re: The sequence S is defined by Sn – 1 = (Sn) for each integer
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12 Aug 2018, 04:42
12 Aug 2018, 04:42
1
Expert Reply
Explanation
The sequence \(S_{n – 1} = \frac{1}{4}(S_n)\) can be read as “to get any term in sequence S, multiply the term after that term by \(\frac{1}{4}\).” Since this formula is “backwards” (usually, later terms are defined with regard to previous terms), solve the formula for \(S_n\):
\(S_{n – 1} = \frac{1}{4}(S_n)\)
\(4S_{n – 1} = S_n\)
\(S_n = 4S_{n – 1}\)
This can be read as “to get any term in sequence S, multiply the previous term by 4.”
The problem gives the first term and asks for the fourth:
To get \(S_2\), multiply the previous term by 4: \((4)(-4) = -16\). Continue this procedure to find each subsequent term. Therefore, \(S_3 = (4)(-16) = -64\). \(S_4 = (4)(-64) = -256\):
The sequence \(S_{n – 1} = \frac{1}{4}(S_n)\) can be read as “to get any term in sequence S, multiply the term after that term by \(\frac{1}{4}\).” Since this formula is “backwards” (usually, later terms are defined with regard to previous terms), solve the formula for \(S_n\):
\(S_{n – 1} = \frac{1}{4}(S_n)\)
\(4S_{n – 1} = S_n\)
\(S_n = 4S_{n – 1}\)
This can be read as “to get any term in sequence S, multiply the previous term by 4.”
The problem gives the first term and asks for the fourth:
| -4 | |||
| \(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) |
To get \(S_2\), multiply the previous term by 4: \((4)(-4) = -16\). Continue this procedure to find each subsequent term. Therefore, \(S_3 = (4)(-16) = -64\). \(S_4 = (4)(-64) = -256\):
| -4 | -16 | -64 | -256 |
| \(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) |
Re: The sequence S is defined by Sn – 1 = (Sn) for each integer
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10 May 2020, 03:49
10 May 2020, 03:49
A nice little trick here is to multiply both sides by 4 so it all reads well.
