Harmonic_Progression.cpp

/*
        HARMONIC PROGRESSION

        Any sequence of elements where the difference between any
        two consecutive elements is equal is termed to be in A.P.
        Harmonic progression is a sequence of quantities whose
        reciprocals are in arithmetical progression.
        The nth term of an H.P. is defined as 1/(a + (n - 1)*d)
        where a is the first element of the A.P.
        d is the common difference of the A.P.
*/

#include<bits/stdc++.h>
using namespace std;

int main() {
    cout << "Enter the First Term of A.P.";
    int a;
    cin >> a;
    cout << "Enter the common difference";
    int d;
    cin >> d;
    cout << "Enter N (The index of term to find)";
    int n;
    cin >> n;
    cout << "The term at index " << n << " of H.P. is 1/" << (a + (n - 1) * d);
}

/*
    INPUT : a = 5
            d = 2
            n = 7
    OUTPUT : The term at index 7 of H.P. is 1/17
    VERIFICATION : The A.P. would be 5,7,9,11,13,15,17...
                   so H.P. would be 1/5, 1/7, 1/9, 1/11, 1/13, 1/17....
*/