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The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for
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25 Jul 2018, 17:25
25 Jul 2018, 17:25
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The sequence S is defined by \(S_n = S_{n – 1} + S_{n – 2} – 3\) for each integer n ≥ 3. If \(S_1 = 5\) and \(S_2 = 0\), what is the value of \(S_6\)?
(A) –6
(B) –5
(C) –3
(D) –1
(E) 1
(A) –6
(B) –5
(C) –3
(D) –1
(E) 1
Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 3 for
[#permalink]
11 Aug 2018, 16:54
11 Aug 2018, 16:54
Expert Reply
Explanation
The sequence \(S_n = S_{n – 1} + S_{n - 2} - 3\) can be read as “to get any term in sequence S, sum the two previous terms and subtract 3.”
The problem gives the first two terms and asks for the sixth term:
To get any term, sum the two previous terms and subtract 3. So the third term will equal 5 + 0 – 3 = 2.
The fourth term will equal 0 + 2 – 3 = –1. The fifth term will equal 2 + (–1) – 3 = –2. The sixth term will equal –1 + (–2) – 3 = –6:
The sequence \(S_n = S_{n – 1} + S_{n - 2} - 3\) can be read as “to get any term in sequence S, sum the two previous terms and subtract 3.”
The problem gives the first two terms and asks for the sixth term:
| 5 | 0 | ||||
| \(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) | \(S_6\) |
To get any term, sum the two previous terms and subtract 3. So the third term will equal 5 + 0 – 3 = 2.
The fourth term will equal 0 + 2 – 3 = –1. The fifth term will equal 2 + (–1) – 3 = –2. The sixth term will equal –1 + (–2) – 3 = –6:
| 5 | 0 | 2 | -1 | -2 | -6 |
| \(S_1\) | \(S_2\) | \(S_3\) | \(S_4\) | \(S_5\) | \(S_6\) |
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Re: The sequence S is defined by Sn = Sn 1 + Sn 2 3 for
[#permalink]
20 Sep 2022, 08:40
20 Sep 2022, 08:40
1
Given that \(S_n = S_{n - 1} + S_{n - 2} - 3\), \(S_1 = 5\) and \(S_2 = 0\) and we need to find the value of \(S_6\)
\(S_3 = S_{3 - 1} + S_{3 - 2} - 3\) = \(S_{2} + S_{1} - 3\) = Sum of previous two terms - 3 = 0 + 5 - 3 = 2
\(S_4\) = \(S_3\) + \(S_2\) - 3 = 2 + 0 - 3 = -1
\(S_5\) = \(S_4\) + \(S_3\) - 3 = -1 + 2 - 3 = -2
\(S_6\) = \(S_5\) + \(S_4\) - 3 = -2 + -1 - 3 = -6
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Sequence problems
\(S_3 = S_{3 - 1} + S_{3 - 2} - 3\) = \(S_{2} + S_{1} - 3\) = Sum of previous two terms - 3 = 0 + 5 - 3 = 2
\(S_4\) = \(S_3\) + \(S_2\) - 3 = 2 + 0 - 3 = -1
\(S_5\) = \(S_4\) + \(S_3\) - 3 = -1 + 2 - 3 = -2
\(S_6\) = \(S_5\) + \(S_4\) - 3 = -2 + -1 - 3 = -6
So, Answer will be A
Hope it helps!
Watch the following video to learn How to Sequence problems
