Question

How many natural numbers are there between 400 and 700 which are divisible by 9.

Answer 1

Solution:

The first number greater than 400 and divisible by 9 = 405
405/9 = 45

The last number less than 700 and divisible by 9 = 693
693/9 = 77

This is in the A.P.Series:
405, 405+9=414, 423, ……… , 693.

We know that nth term of an A.P. Series is:
tn = a+(n-1)d
a = first term = 405
d = common difference = 9
tn = last term = 693
n = no. of terms

or, 693 = 405+(n-1)9
or, (n-1)9 = 693-405
or, (n-1)9 = 288
or, n-1 = 288/9
or, n-1 = 32
or, n = 32+1
or, n = 33

There are 33 natural numbers between 400 and 700 which are divisible by 9.
(Answer)