How many three digit numbers are divisible by 7?

Solution:

In this problem, we need to find out how many numbers of three digits are divisible by 7.

So, we know that the first three digit number that is divisible by 7 is 105 and the last three digit number divisible by 7 is 994. Also, all the terms which are divisible by 7 will form an A.P. with the common difference of 7.

So here,

First term (a) = 105

Last term (an) = 994

Common difference (d) = 7

So, let us take the number of terms as n

Now, as we know,

$a_{n}=a+(n-1) d$

So, for the last term,

$994=105+(n-1) 7$

$994=105+7 n-7$

$994=98+7 n$

$994-98=7 n$

Further simplifying,

$896=7 n$

$n=\frac{896}{7}$

$n=128$

Therefore, the number of three digit terms divisible by 7 is 128 .