Question 1132599


How many 3 digit positive integers exist that when divided by 3 leave a reminder of 2?

Least 3 digit number is {{{100}}}.

Since divisor is {{{3}}}, & remainder {{{2}}}

.
{{{3*33+2=101}}}

next number will be  {{{3*34+2=104 }}}

next will be  {{{3*35+2=107}}}
 
the last {{{3}}} digit number leaving remainder{{{ 2}}}, while dividing by {{{3}}} is {{{998}}}

Sequence : {{{101}}}, {{{104}}},{{{107}}},.......,{{{998}}}
common difference: {{{d=3}}}

use nth term formula:

{{{a[n]=a[1]+d(n-1)}}}

where {{{a[1]}}}= 1st term, {{{d}}}= common difference, & {{{n }}}is the term

=> {{{101 + (n-1)*3 = 998}}}

=> {{{ (n-1)*3 = 998-101}}}

=> {{{3n - 3 = 897}}}

=> {{{3n = 900}}}

=> {{{n = 300}}}

So, there are {{{300}}} such numbers ………..ANS