Question

How many three digit numbers are divisible by 7 ? easy solution​

Answer 1

Step-by-step explanation:

The first 3-digit number which is divisible by 7 is 105

The last 3-digit number which is divisible by 7 is 994

The list of 3-digit numbers divisible by 7 are

105, 112, 119,…..994 which forms an A.P

Consider a formula

Answer 2

${\huge{\star{\underbrace{\tt{\red{Answer}}}}}}{\huge{\star}}$

First 3 digit number divided by 7 = 105

Second 3 digit number divided by 7 = 112

Last 3 digit number divided by 7 = 994

Now,

105 , 112 , . . . . 994 forms an AP

hence

$\star \: \: \sf{first \: term \: ( a_{1}) = 105}$

$\star \: \: \sf{second \: term \: ( a_{2}) = 112}$

$\star \: \: \sf{last \: term \: ( a_{n}) = 994}$

$\star \sf \: \: common \: difference \: (d) = a_{2} - a_{1} \implies 112 - 102 = 7$

Formula of AP :

${\boxed{ \green{\sf \: a_{n} = a_{1} + (n - 1)d}}}$

$: \Longrightarrow \sf \: 994 = 105 + (n - 1)7$

$: \Longrightarrow \sf \: 994 - 105 = (n - 1)7$

$: \Longrightarrow \sf \: \cancel \frac{889}{7} = n - 1$

$: \Longrightarrow \sf \: 127 = n - 1$

$: \Longrightarrow \sf \: 127 + 1 = n$

$: \Longrightarrow \sf \: n = 128$

Hence the number of 3 digit numbers divided by 7 is 128.

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