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Arithmetic Progressions

Question
CBSEENMA10009719

How many three-digit natural numbers are divisible by 7?

Solution

Three digit numbers divisible by 7 are 

105, 112, 119, .......994

This is an AP with first term (a) =105 and comman difference (d)= 7

an be the last term.an  = a+ (n - 1 )994 = 105 + (n - 1 ) ( 7 )7 ( n - 1 ) =889n - 1 = 127n = 128Thus, there are 128 three-digit natural terms that are divisible by 7.