Positive integers congruent to 1 modulo 9 are 1,10,19,28, 37, 46, 55,...,991, 1000
This is an arithmetic series where \(a_1=1,a_n=1000,d=9,n=?\)
\(a_n=a_1+(n-1)d
\\1000=1+(n-1)9
\\999=9(n-1)
\\111=n-1
\
=112\)
Total number of positive integers congruent to 1 modulo 9 is 112.