Question

find no of all three digit natural no which are divisible by 7 and leaves remainder 3
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Answer 1

first three digit number is 100

if 100 divides by 7 then remainder is 2

so 101 is the first number who when divides by 7 remaining 3

next number must be greater by 7

so it is 108

so series is

101 , 108 , 115 ,.........

last three digit number is 999 when divides by 7 remaining 5

so 997 is the number when divides by 7 remaining 3

so series is

101 , 108 , 115 ,......... ,997

here a = 101

d = 7

tn = 997

n = ?

tn = a + (n-1) d

997 = 101 + ( n - 1 ) × 7

997 - 101 = ( n - 1 ) × 7

( n - 1 ) × 7 = 896

n - 1 = 896 / 7

n - 1 = 128

n = 128 + 1

n = 129

so 129 numbers

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