Which number follows the sequence?

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11 , 2047 , 88573 , 1398101 , 12207031 , 72559411 , 329554457 , 1227133513 , 3922632451 , ?

Which number follows this sequence?


The answer is 11111111111.

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1 solution

Ashish Menon
Mar 26, 2016

The numbers are of the form :-
n 10 + n 9 + n 8 + n 7 + n 6 + n 5 + n 4 + n 3 + n 2 + n + 1 n^{10} + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1

So, for n = 1 n = 1 , the number is 11 11
So, for n = 2 n = 2 , the number is 2047 2047
So, for n = 3 n = 3 , the number is 88573 88573
So, for n = 4 n = 4 , the number is 1398101 1398101
So, for n = 5 n = 5 , the number is 12207031 12207031
So, for n = 6 n = 6 , the number is 72559411 72559411
So, for n = 7 n = 7 , the number is 329554457 329554457
So, for n = 8 n = 8 , the number is 1227133513 1227133513
So, for n = 9 n = 9 , the number is 3922632451 3922632451

So, in the number we need, n = 10 n = 10 .
So, the number is 10 10 + 10 9 + 10 8 + 10 7 + 10 6 + 10 5 + 10 4 + 10 3 + 10 2 + 10 + 1 {10}^{10}+{10}^9+{10}^8+{10}^7+{10}^6+{10}^5+{10}^4+{10}^3+{10}^2+10+1
= 10000000000 + 1000000000 + 100000000 + 10000000 + 1000000 + 100000 + 10000 + 1000 + 100 + 10 + 1 10000000000+1000000000+100000000+10000000+1000000+100000+10000+1000+100+10+1
= 11111111111 \boxed {11111111111}

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