MHB Solve the Sequence Challenge: Find the Missing Digit & a Term

[anemone]

There is a sequence which has the first 3 terms listed as $1,\,94095,\,5265679\cdots$.

The 50th term has all but one digit. If the missing digit is $a$, find the $a$th term from this sequence.

 

[anemone]

My solution:

Spoiler

Rewrite the sequence by reversing the digits of the numbers listed in the given sequence, we have:

$1,\,59049,\,9765625,\cdots=1^{10},\,3^{10},\,5^{10},\,\cdots$ with its general term defined as $b_n=(2n-1)^{10}$.

So, $b_{50}=(2(50)-1)^{10}=99^{10}=90438207500880449001$ and the missing digit is $a=6$.

Thus, the sixth term of this sequence is the reversed order from $b_6=(2(6)-1)^{10}=25937424601$, i.e. 10642473952.

 

[Opalg]

[sp]So to get the sixth term of the original sequence, you should reverse the digits of $b_6$ to get $10642473952$. (Wink) (Bigsmile) [/sp]

 

[anemone]

[sp]So to get the sixth term of the original sequence, you should reverse the digits of $b_6$ to get $10642473952$. (Wink) (Bigsmile) [/sp]

Thank you so very much, Opalg for pointing out one most obvious careless stupid mistake of mine, hehehe...since today I have made two cups of coffee for kaliprasad and MarkFL, I'm sorely tempted to make you too another cup of coffee, hehehe...

 

[Opalg]

Thank you so very much, Opalg for pointing out one most obvious careless stupid mistake of mine, hehehe...since today I have made two cups of coffee for kaliprasad and MarkFL, I'm sorely tempted to make you too another cup of coffee, hehehe...

Mmmm... just what I like best. As it happens, we visited Bettys of Harrgate today, to buy some of their Java Kalibaru coffee. So we'll think of you as we drink it. (Mmm)