3
$\begingroup$

Find the next number in the sequence:

$10,11,21,32,53,85,49,45,5,50,?$

This sequence seems to me as possibly difficult to guess, so below is a hint.

The sequence is about remainders.

$\endgroup$
3
$\begingroup$

Well, let me try...

(10 + 11) % 89 = 21 % 89 = 21
(11 + 21) % 89 = 32 % 89 = 32
(21 + 32) % 89 = 53 % 89 = 53
(32 + 53) % 89 = 85 % 89 = 85
(53 + 85) % 89 = 138 % 89 = 49
(85 + 49) % 89 = 134 % 89 = 45
(49 + 45) % 89 = 94 % 89 = 5
(45 + 5) % 89 = 50 % 89 = 50

So, the next one should be...

(5 + 50) % 89 = 55 % 89 = 55

$\endgroup$
  • 2
    $\begingroup$ That is correct! I was thinking of $10^n\% 89$, but your pattern also works. $\endgroup$ – Jason Kim May 2 at 4:25
  • 1
    $\begingroup$ $10^n~\%~89 = 100 \times 10^{n-2}~\%~89 = 11 \times 10^{n-2}~\%~89 = (10^{n-1} + 10^{n-2})~\% 89$ $\endgroup$ – athin May 2 at 4:31
  • $\begingroup$ I noticed that when I thought about why your solution worked. If I had seen that pattern, I could have computed the terms so much easier... $\endgroup$ – Jason Kim May 2 at 5:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.