Find the next three in the sequence: 0.3333..., 0.3, 0.252525..., 0.222..., 0.2, 0.131313..., ?, ?, ?

(In reply to Answer by K Sengupta)

The pth term of the given sequence is constituted by expressing the
fraction 1/3 in base (11-p)

Denoting pth term of the given sequence as S(p), we have:

S(1) = (1/3)_10 = (0.3333...)_10
S(2) = (1/3)_10 = (0.3)_9
S(3) = (1/3)_10 = (0.2525253...)_8
S(4) = (1/3)_10 = (0.222...)_7
S(5) = (1/3)_10 = (0.2)_6
S(6) = (1/3)_10 = (0.131313...)_5
S(7) = (1/3)_10 = (0.111...)_4
S(8) = (1/3)_10 = (0.1)_3
S(9) = (1/3)_10 = (0.010101...)_2

Consequently, required next three numbers in the sequence are 0.111..., 0.1 and  0.010101... 

Edited on April 29, 2008, 4:00 pm

Posted by K Sengupta on 2008-03-24 01:12:46