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**