What are the next two numbers in the sequence?
1, 4, 9, 14, 21, 30, 41, 54, __, __

(In reply to Answer by K Sengupta)

The given numbers inclusive of each term are expressed in duodecimal (base 12) system.

Converting each of the terms to the decimal system, the terms of the given sequence are:

1, 4, 9, 16, 25, 36, 49, 64

The above numbers are simply the squares of positive integers 1,2, ...., 8

Accordingly, the next two numbers in decimal notation must be equal to 9^2= 81 and 10^2 = 100

Converting 81 and 100 into base 12, we obtain 69 and 84 as the required next two terms.

 

Posted by K Sengupta on 2008-03-29 22:58:31