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Sum of first N natural numbers which are divisible by 2 and 7 in C++
In this problem, we are given a number N. Our task is to find the sum of first N natural numbers which are divisible by 2 and 7.
So, here we will be given a number N, the program will find the sum of numbers between 1 to N that is divisible by 2 and 7.
Let’s take an example to understand the problem,
Input −
N = 10
Output −
37
Explanation −
sum = 2 + 4 + 6 + 7 + 8 + 10 = 37
So, the basic idea to solve the problem is to find all the numbers that are divisible by 2 or by 7. This sum will be −
Sum of numbers divisible by 2 + sum of numbers divisible by 7 - sum of number divisible by 14.
All these sums can be generated using A.P. formulas,
S2 = [( (N/2)/2) * ( (2*2)+((N/2-1)*2) )] S7 = [( (N/7)/2) * ( (2*7)+((N/7-1)*7) )] S14 = [( (N/14)/2) * ( (2*14)+((N/2-1)*14) )]
The final sum,
Sum = S2 + S7 - S14 Sum = [( (N/2)/2) * ( (2*2)+((N/2-1)*2) )] + [( (N/7)/2) * ( (2*7)+((N/7-1)*7) )] - [( (N/14)/2) * ( (2*14)+((N/2-1)*14) )]
Example
Program to illustrate the solution,
#include <iostream> using namespace std; int findSum(int N) { return ( ((N/2)*(2*2+(N/2-1)*2)/2) + ((N/7)*(2*7+(N/7-1)*7)/2) - ((N/14)*(2*14+(N/14-1)*14)/2) ); } int main(){ int N = 42; cout<<"The sum of natural numbers which are divisible by 2 and 7 is "<<findSum(N); return 0; }
Output
The sum of natural numbers which are divisible by 2 and 7 is 525
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