How many three-digit numbers are divisible by | vedclass

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Question

(C) The first three-digit number divisible by $7$ is $105$.The next numbers are $105 + 7 = 112, 112 + 7 = 119, \ldots$These numbers form an Arithmetic

Vedclass · Accepted Answer

$128$

Vedclass · Answer

(C) The first three-digit number divisible by $7$ is $105$.The next numbers are $105 + 7 = 112, 112 + 7 = 119, \ldots$These numbers form an Arithmetic Progression $(A.P.)$ where the first term $a = 105$ and the common difference $d = 7$.The largest three-digit number is $999$. Dividing $999$ by $7$,we get $999 = 7 	imes 142 + 5$. The remainder is $5$.Thus,the largest three-digit number divisible by $7$ is $999 - 5 = 994$.Let $994$ be the $n^{th}$ term of the $A.P.$ sequence.Using the formula $a_n = a + (n - 1)d$:$994 = 105 + (n - 1)7$$994 - 105 = (n - 1)7$$889 = (n - 1)7$$n - 1 = 889 / 7$$n - 1 = 127$$n = 128$Therefore,there are $128$ three-digit numbers divisible by $7$.

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

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