BdMO Online Forum

0,1,2,10,11,12,20....এই ধারার 50 তম পদটি কত ?

The given sequence consists of $3$ distinct sequences,namely $(0,10,20,...),(1,11,21,...),(2,12,22,...)$. So $50$th term of the given sequence will be the $17$th term of the second sequence here and it is $161$.

আমিও প্রথমে 161 বের করেছিলাম। পরে গুগল করে দেখি 0,1,2,10,11,12,20...এই ধারাটা আসলে base 3 ধরে 0,1,2,3,4,5,6,...অর্থাত্‍ ডেসিমেলের অনুরূপ। ফলে (49)10 কে base 3 তে কনভার্ট করতে হবে।

simu wrote:আমিও প্রথমে 161 বের করেছিলাম। পরে গুগল করে দেখি 0,1,2,10,11,12,20...এই ধারাটা আসলে base 3 ধরে 0,1,2,3,4,5,6,...অর্থাত্‍ ডেসিমেলের অনুরূপ। ফলে (49)10 কে base 3 তে কনভার্ট করতে হবে।

Now,if you consider it from this point of view,the answer will be $1211$. But where is the problem in your first solution? For example,if I tell you to calculate the next term of the sequence $1,2,4,8,16,...$ what will your answer be? $32$ ? Check the following:

$49/3$ ; Remainder 1, Quotient 16

$16/3$ ; Remainder 1, Quotient 5

$5/3$ ; Remainder 2, Quotient 1

$1/3$ ; Remainder 1

So the 50th term in (base 3) is $1211$.

I suggest that, any sequence depends only what is given.
suppose, I give you $1$
what is next ?
$2$ ? $3$ ? $4$ ? $11$ ? $10$ ?
each and every has some logic behind it.
Of course it is true that just $1$ can't be a sequence or series,
what I want to say is any logic that satisfies what is given should be right.
None can claim none.
As much as I know when such series are given, they try to find all possible logics, or try to give something that can have only one answer.

nafistiham wrote:what I want to say is any logic that satisfies what is given should be right.

As much as I know when such series are given, they try to find all possible logics, or try to give something that can have only one answer.

The very thing I wanted to tell.

তিহাম ভাইয়ার সাথে আমিও একমত। এই সিরিজকে একমুখী করার জন্য অন্তত আরও তিনটি টার্ম দেওয়া উচিত ছিল। তাহলে বোঝা যেত যে এতে $22$এর পরে $30$ না এসে $100$ আসছে। তখন হয়ত বিষয়টি অন্যরকম হত।

nafistiham wrote:I suggest that, any sequence depends only what is given.
suppose, I give you $1$
what is next ?
$2$ ? $3$ ? $4$ ? $11$ ? $10$ ?

অথবা ইন্টারপোলেশন মাইরা একটা polynomial আনা যায়

Answer is maybe $1001$.