Question

How many natural numbers are there between 123 and 999 completely divisuble by 7?

Answer 1

Here, equation of AP will be used.
where,
a=126(first number after 123, divisible by7)
d=7
nth term(An)= 994(last number before 999, divisible by 7)

(A and An are calculated by hit and trial method)

An=a+(n-1)d
994=126+(n-1)7
994-126=7n-7
868+7=7n
875=7n
n=875/7
n=125

So, in between 123 & 999, there are exactly 125 numbers which are completely divisible by 7