The sequence:

1, 3, 7, 13, 21, ...

What is the 600th member of the series?

What member, above the first, with fewer than 5 digits, is a perfect cube?

What member is a 5-digit palindrome that can also be read as a binary number?

What's the smaller of the two consecutive members that are 1000 apart?

The nth term of the sequence can be expressed as: n^2-n+1. So 600th member is 359401.
The second question can be solved by examining the equation n^2-n+1=k^3 from which one gets constraints for k. After a little testing the only possible value for k is 7 => n=19. So the asked member is 343.
For the 3th question there are only 4 possible choices  (11111,10001,11011 and 10101) and by solving n^2-n+1=11111 and so on we see that 10101 is the only possible solution (n=101).
The final question can be solved from equation n(n-1)+1000=n(n+1) => n=500.

Posted by atheron on 2007-05-07 10:40:57