how many 3 digit number are there which leave remainder 3 on division by 7.


please say the answer step by step​

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1. Answer:

   hey here is your solution

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   so here we go

   Step-by-step explanation:

   so the three digit number which when divided by 7 leaves remainder 3 are 101,108,115,up to ,997

   now here t1=101 t2=108 t3=115

   so d1=t2-t1

   =108-101

   =7

   also,,

   d2=t3-t2

   =115-108

   =7

   so as common difference is constant and would be constant in next terms also

   it forms an ap ie a sequence of arithmetic progression

   so here we have to find n ie total possible terms

   so for above ap,

   a=t1=101 d=7

   tn=997

   so use formula

   tn=a+(n-1)d

   ie 997=101+[(n-+)×7]

   997=(101-7)+7n

   ie 7n=997-94

   ie 7n=903

   so n=129

   hence in total there are 129 3 digit number which leaves remainder as 3 when divided by 7

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