Question

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


please say the answer step by step​

Answer 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