What is the 1000th positive integer with an odd number of digits?
I do not think our guest has interpreted the question as it is written, I think he/she has found the 1000th odd integer, not the 1000th integer with an odd number of digits.
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there are 9 one digit numbers. 1-9 9-1+1=9
there are 900 three digit numbers 100-999 999-100+1=900
that is 909 altogether
So the 1000th one will have 5 digits.
1000-909=91
10000 is the 910th one,
10090 is the 1000th one.
1000th term = First term + [Number of term - 1] x Common difference.
1,000th = 1 + [1,000 - 1] x 2
1,000th = 1 + [999 x 2]
1,000th= 1 + 1,998
1,000th term =1,999
I do not think our guest has interpreted the question as it is written, I think he/she has found the 1000th odd integer, not the 1000th integer with an odd number of digits.
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there are 9 one digit numbers. 1-9 9-1+1=9
there are 900 three digit numbers 100-999 999-100+1=900
that is 909 altogether
So the 1000th one will have 5 digits.
1000-909=91
10000 is the 910th one,
10090 is the 1000th one.