Find the sum of first N terms of the series 2, 5, 8, 11, 14..
Last Updated :
19 Apr, 2023
Given a positive integer N, the task is to find the sum of the first N terms of the series
2, 5, 8, 11, 14..
Examples:
Input: N = 5
Output: 40
Input: N = 10
Output: 155
Approach:
1st term = 2
2nd term = (2 + 3) = 5
3rd term = (5 + 3) = 8
4th term = (8 + 3) = 11
.
.
Nth term = (2 + (N – 1) * 3) = 3N – 1
The sequence is formed by using the following pattern. For any value N-
Here,
a is the first term
d is the common difference
The above solution can be derived following the series of steps-
The series-
2, 5, 8, 11, …., till N terms
is in A.P. with first term of the series a = 2 and common difference d = 3
Sum of N terms of an A.P. is
Illustration:
Input: N = 5
Output: 40
Explanation:
a = 2
d = 3
Below is the implementation of the above approach:
C++
#include <iostream>
using namespace std;
int nth( int n, int a1, int d)
{
return (a1 + (n - 1) * d);
}
int sum( int a1, int nterm, int n)
{
return n * (a1 + nterm) / 2;
}
int main()
{
int N = 5;
int a = 2;
int d = 3;
int nterm = nth(N, a, d);
cout << sum(a, nterm, N) << endl;
return 0;
}
|
C
#include <stdio.h>
int nth( int n, int a1, int d)
{
return (a1 + (n - 1) * d);
}
int sum( int a1, int nterm, int n)
{
return n * (a1 + nterm) / 2;
}
int main()
{
int N = 5;
int a = 2;
int d = 3;
int nterm = nth(N, a, d);
printf ( "%d" , sum(a, nterm, N));
return 0;
}
|
Java
import java.io.*;
class GFG {
public static void main(String[] args)
{
int N = 5 ;
int a = 2 ;
int d = 3 ;
int nterm = nth(N, a, d);
System.out.println(sum(a, nterm, N));
}
public static int nth( int n,
int a1, int d)
{
return (a1 + (n - 1 ) * d);
}
public static int sum( int a1,
int nterm, int n)
{
return n * (a1 + nterm) / 2 ;
}
}
|
Python3
def nth(n, a1, d):
return (a1 + (n - 1 ) * d);
def sum (a1, nterm, n):
return n * (a1 + nterm) / 2 ;
N = 5 ;
a = 2 ;
d = 3 ;
nterm = nth(N, a, d);
print (( int )( sum (a, nterm, N)))
|
C#
using System;
public class GFG
{
public static int nth( int n, int a1, int d)
{
return (a1 + (n - 1) * d);
}
public static int sum( int a1, int nterm, int n)
{
return n * (a1 + nterm) / 2;
}
static public void Main()
{
int N = 5;
int a = 2;
int d = 3;
int nterm = nth(N, a, d);
Console.Write(sum(a, nterm, N));
}
}
|
Javascript
<script>
function nth(n, a1, d) {
return (a1 + (n - 1) * d);
}
function sum(a1, nterm, n) {
return n * (a1 + nterm) / 2;
}
let N = 5;
let a = 2;
let d = 3;
let nterm = nth(N, a, d);
document.write(sum(a, nterm, N) + '<br>' );
</script>
|
Time complexity: O(1) because performing constant operations
Auxiliary Space: O(1) // since no extra array or recursion is used so the space taken by the algorithm is constant
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