Problem Statement: Given an A.P. Series, we need to find the sum of the Series.

a = first term of A.P.

d= common Difference of A.P.

n= Number of Terms in  A.P.

Examples:

Example 1:
Input:
n=4
a=2
d=2
Output: 20
Explanation: 2+4+6+8 = 20

Input:
n=8
a=2
d=5
Output: 124
Explanation: -2 +3 + 8 + 13 + 18 + 23 + 28 + 33 = 124

What is A.P. (Arithmetic Progression)?

A.P. is the series of terms having the first term as a and d, common difference. Every next term in the A.P. is greater than the previous term by d units.

Example – 

-2, 3 , 8 , 13 , 18 , 23 , 28 , 33

First term , a = – 2

Common Difference , d=5

Last term , a_n=33

Solution

Disclaimer: Don’t jump directly to the solution, try it out yourself first.

Solution 1: Using Loops

Approach: This approach consists of simply adding elements by moving them for a loop. We create a sum variable and add the terms one by one to get the sum of the A.P. Series.

For Example, 

a=2 , d=4, n=5

So run the loop 5 times.

Code:

#include <bits/stdc++.h>
using namespace std;
float sumofAp(float a, float d, int n)
{
    float sum = 0;
    for (int i = 1; i <= n; i++)
    {
        sum += a;
        a += d;
    }
    return sum;
}
int main()
{
    float a = 1.5, d = 3;
    int n = 5;
    cout << "Sum of Given Ap Series: " << sumofAp(a, d, n) << endl;
}

import java.util.*;
class TUF{
static double sumofAp(double a, double d, int n)
{
    double sum = 0.0;
    for (int i = 1; i <= n; i++)
    {
        sum += a;
        a += d;
    }
    return sum;
}
public static void main(String args[])
{
    double a = 1.5, d = 3;
    int n = 5;
    System.out.println("Sum of Given Ap Series: "+sumofAp(a, d, n));
}
}

Solution 2: Using Formula

Approach: This approach is now a time as well as a space-optimized approach since we are going to use the direct formula for this.

Code:

#include <bits/stdc++.h>
using namespace std;
float sumofAp(float a, float d, int n)
{
     float sum = (n / 2.0) * (2.0 * a + (n - 1) * d);
    return sum;

}
int main()
{
    float a = 1.5, d = 3, n = 5;
    cout << "Sum of Given Ap Series: " << sumofAp(a, d, n) << endl;
}

Output:

Sum of Given Ap Series: 37.5

Time Complexity: O(1) since we are using direct formula

Space Complexity: O(1) since no extra space is required

import java.util.*;
class TUF{
static double sumofAp(double a, double d, int n)
{
   double sum = (n / 2.0) * (2.0 * a + (n - 1) * d);
    return sum;
}
public static void main(String args[])
{
    double a = 1.5, d = 3;
    int n = 5;
    System.out.println("Sum of Given Ap Series: "+sumofAp(a, d, n));
}
}

Special thanks to Gurmeet Singh for contributing to this article on takeUforward. If you also wish to share your knowledge with the takeUforward fam, please check out this article