perplexus.info :: Sequences : A recursive game

A recursive game (Posted on 2017-10-27)

Find the full definition of a_n in terms of a_n-1 given a₁=1.
The first 7 terms are:

1, 3, 8, 9, 4, 5, 10 ...

How does it continue?

No Solution Yet Submitted by Ady TZIDON

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Some solution like (but non the intended one)

Comment 1 of 1

Taking the first three terms 1,3,8 as basis for the sequence:

a4 = a1 + a3 = 1+8 = 9

a5 = a1 + a2 = 1+3 = 4

a6 = a1 + a5 = 1+4 = 5

a7 = a1 + a4 = 1+9 = 10

Generalizing

a(n) = a1 + a((n-2)+(-1)^n))

for n>3

Accordingly next terms:

a8 = a1 + a7 = 11

a9 = a1 + a6 = 6

Is this is the intended solution?

Edited on December 10, 2017, 3:36 pm

Posted by armando on 2017-12-10 12:44:28

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