find the number of natural number between 102and 998 which are divisible
Answers
Answer:
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Step-by-step explanation:
Given,
The number should be divisible by 2 and 5 both.
LCM of 2 and 5 = 10
It means numbers divisible by 10 are divisible by both 2 and 5.
Method 1: Basic Maths
Total number of numbers divisible by 10 from 1 to 998 = 998 / 10 = 99
Numbers divisible by 10 from 1 to 102 = 102 / 10 = 10
Numbers between 102 and 998 divisible by both 2 and 5 = Total number of numbers divisible by 10 from 1 to 998 - Numbers divisible by 10 from 1 to 102
Numbers between 102 and 998 divisible by both 2 and 5 = 99 - 10 = 89
Method 2: Arithmetic Progression
Arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
Example:
10, 20, 30, 40, 50 are in AP as the difference between the consecutive terms is 10.
The numbers divisible by 10 between 102 and 998 are 110, 120, 130, 140, 150, …….990.
If the first term of the AP is known and common difference is known then the nth term can be found as below:
a(n) = a1 + (n-1)*d
where,
a1 is the first term of the series, a1 = 110
d is difference between the consecutive terms, d = 10
a(n) is the nth term of the series, a(n) = 990
n is the number of the term, n = ?
The general formula to find the nth term of the AP is:
a(n) = a(m) + (n-m)*d
Putting the values into the formula,
990 = 110 + (n-1)*10
880 = (n-1) * 10
88 = n-1
n = 88 + 1 = 89
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