Math, asked by sanket796, 1 year ago

sum of 3 digit numbers divisible by 7

Answers

Answered by devyash6003
71
This is the answer for your question
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Answered by mysticd
82

Answer:

Sum \:of \:3\:digit \: numbers\\divisible \:by \:7 = 70336

Step-by-step explanation:

100,101,102,...,999 are 3 digit numbers.

105, 112, 119,....,994 are 3 digit numbers divisible by 7.

first term (a) = 105,

Last term (l) = 994

 common\: difference (d)\\=a_{2}-a_{1}\\=112-105\\=7

 l = 994

\implies a+(n-1)d = 994

\implies 105+(n-1)7= 994

/* Divide each term by 7, we get

\implies 15+n-1 = 142

\implies14+n=142

\implies n = 142 - 14

\implies n = 128

 Sum \:of \:n \:terms(S_{n})=\frac{n}{2}(a+l)

\implies S_{128}=\frac{128}{2}(105+994)

= 64\times 1099

=70336

Therefore,

Sum \:of \:3\:digit \: numbers\\divisible \:by \:7 = 70336

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