dawn6251 dawn6251

20-05-2018
Mathematics

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The lucas sequence is the sequence 1, 3, 4, 7, 11, $\ldots$ where the first term is 1, the second term is 3 and each term after that is the sum of the previous two terms. what is the remainder when the $100^{\mathrm{th}}$ term of the sequence is divided by 8?

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sqdancefan sqdancefan

20-05-2018

Mod 8, the sequence repeats after 12 terms:
1 3 4 7 3 2 5 7 4 3 7 2

Thus the 100th term, mod 8, will be the 4th term of this sequence: 7

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