Question

find the term of natural numbers amongst first 1000 numbers which are neither divisible by 2 nor 5​

Answer 1

considering the question to be
"Find number of natural numbers amongst first 1000 numbers which are neither divisible by 2 nor

Total natural numbers= 1000

Number of natural numbers div by 2:-

2,4,6,8..........1000
Using Formula of nth term in arithmetic progression
1000= 2 +(n-1)2
998/2=n-1
n= 500


Number of natural numbers div by 5:-

5,10,15,20.........1000
Using Formula of nth term in arithmetic progression
1000= 5 +(n'-1)5
995/5=n'-1
n'= 200

We see the numbers which are divisible by both 2 and 5 have been counted twice.
Therefore we subtract numbers divisible by (2*5) from n +n'


Number of natural numbers div by 10:-

10,20.........1000
Using Formula of nth term in arithmetic progression
1000= 10 +(t-1)10
990/10=t-1
t= 100

Therfore required answer
= 1000-( n + n' - t)
= 100-600
=400


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