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14 May 2020, 01:02
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\(s_{1}\): -3
\(s_{4}\): -7
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Difficulty:
55%
(hard)
Question Stats:
71% (02:43) correct
29%
(02:58)
wrong
based on 2597
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For each positive integer n, the quantity \(s_{n}\) is defined such that \(s_{n + 2} = (s_{n})^2 − s_{n + 1}\). In addition, \(s_{2} = 1\).
Select values for \(s_{1}\) and \(s_{4}\) that are jointly compatible with these conditions. Make only two selections, one in each column.
Select values for \(s_{1}\) and \(s_{4}\) that are jointly compatible with these conditions. Make only two selections, one in each column.
ID: 100402
| \(s_{1}\) | \(s_{4}\) | Values |
| -12 | ||
| -7 | ||
| -3 | ||
| -1 | ||
| 0 |
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Official Answer
\(s_{1}\): -3
\(s_{4}\): -7
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bM22
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14 May 2020, 07:59
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Given: sn+2=(sn)2−sn+1
S2 = 1.
When we substitute values for S3 and S4 we get:
S3 = S1^2 - S2.
S4 = S2^1 - S3 => S4 = S2^1 - S1^2 + S2,
Now Substituting S2 =1, we get:
S4 + S1^2 = 2.
Only 2 values satisfy the given condition: S4 = -7, S1 = -3
S2 = 1.
When we substitute values for S3 and S4 we get:
S3 = S1^2 - S2.
S4 = S2^1 - S3 => S4 = S2^1 - S1^2 + S2,
Now Substituting S2 =1, we get:
S4 + S1^2 = 2.
Only 2 values satisfy the given condition: S4 = -7, S1 = -3
25 Aug 2021, 08:46
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