Find the number of natural numbers between 105 and 995 which are divisible by 2 and 5 both.
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Answer:
The total number of natural numbers is 89.
Step-by-step explanation:
To find : The number of natural numbers between 102 and 998 which are divisible by 2 and 5 both ?
Solution :
The number divisible by 2 and 5 both is the number which is divisible by 10.
The number of natural numbers between 102 and 998 which are divisible by 2 and 5 both are 110,120,130,.... 990 forming an Arithmetic progression.
Where, First term is a=110
The common difference is d=10
The last term is l=990
The last term formula is given by,
l=a+(n-1)dl=a+(n−1)d
990=110+(n-1)10990=110+(n−1)10
990-110=(n-1)10990−110=(n−1)10
880=(n-1)10880=(n−1)10
\frac{880}{10}=n-110880=n−1
n-1=88n−1=88
n=88+1n=88+1
n=89n=89
The total number of natural numbers is 89.
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