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Updated on: 01 Oct 2023, 13:41
Originally posted by Sajjad1994 on 07 Aug 2020, 22:41.
Last edited by BottomJee on 01 Oct 2023, 13:41, edited 2 times in total.
Last edited by BottomJee on 01 Oct 2023, 13:41, edited 2 times in total.
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\(a_{5}\): 16
\(a_{7}\): 53105
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Difficulty:
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18%
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A sequence is defined such that, for all values \(n>3, a_{n}=(a_{n−1})^{2}−(a_{n−2})^{2}.\) If \(a_{1}=1, a_{2}=2\), and \(a_{3}=3\), what are the values of \(a_{5}\) and \(a_{7}\)
| \(a_{5}\) | \(a_{7}\) | |
| 4 | ||
| 5 | ||
| 16 | ||
| 25 | ||
| 52664 | ||
| 53105 |
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Official Answer
\(a_{5}\): 16
\(a_{7}\): 53105
yashikaaggarwal
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Joined: 19 Jan 2020
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07 Aug 2020, 22:48
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A4 = (A3)^2-(A2)^2
A4 = (3)^2-(2)^2
A4 = 9-4
A4 = 5
A5 = (A4)^2-(A3)^2
A5 = (5)^2-(3)^2
A5 = 25-9
A5 = 16
A6 = (A5)^2-(A4)^2
A6 = (16)^2-(5)^2
A6 = 256-25
A6 = 231
A7 = (A6)^2-(A5)^2
A7 = (231)^2-(16)^2
A7 = 53361-256
A7 = 53105
A5 = 16
A7 = 53105
Posted from my mobile device
A4 = (3)^2-(2)^2
A4 = 9-4
A4 = 5
A5 = (A4)^2-(A3)^2
A5 = (5)^2-(3)^2
A5 = 25-9
A5 = 16
A6 = (A5)^2-(A4)^2
A6 = (16)^2-(5)^2
A6 = 256-25
A6 = 231
A7 = (A6)^2-(A5)^2
A7 = (231)^2-(16)^2
A7 = 53361-256
A7 = 53105
A5 = 16
A7 = 53105
Posted from my mobile device
Archit3110
08 Aug 2020, 01:38
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using the given relation
m]n>3, a_{n}=(a_{n−1})^{2}−(a_{n−2})^{2}.[/m] If \(a_{1}=1, a_{2}=2\), and \(a_{3}=3\),
we can find values of a4 which would be
(a3)^2-(a2)^2 ; 5
similarly a5,a6 & a7 can be determined
which would be
a5=16
a6=231 and
a7= 53105
m]n>3, a_{n}=(a_{n−1})^{2}−(a_{n−2})^{2}.[/m] If \(a_{1}=1, a_{2}=2\), and \(a_{3}=3\),
we can find values of a4 which would be
(a3)^2-(a2)^2 ; 5
similarly a5,a6 & a7 can be determined
which would be
a5=16
a6=231 and
a7= 53105
SajjadAhmad
