Question

in the setof 420 natural numbers find the number of integers that are divisible by 7 but not by any 2,3or5.​

Answer 1

Answer:

All three-digit natural numbers which are divisible by 7 are

105,112,119,126,...,994 which are in AP with a=105,d=7,l=994

Let the number of these terms be n. Then,

a

n

=994

a+(n−1)d=994

105+(n−1)×7=994

n=128

Now, S

n

=

2

n

(a+l)

S

n

=

2

128

(105+994)=70336.