Given a number N. The task is to write a program to find the Nth term of the below series:
7, 21, 49, 91, 147, 217, 301, 399, …(N Terms)
Examples:
Input: N = 4
Output: 91
For N = 4
4th Term = ( 7 * 4 * 4 - 7 * 4 + 7)
= 91
Input: N = 10
Output: 636
Given series is:
7, 21, 49, 91, 147, 217, 301, 399, …..
On taking 7 commons from all of the terms, we get:
7 * (1, 3, 7, 13, 21, 31,…..), …..
Now, for the inner-series: 1,3,7,13,21,…
On careful observation we can express the terms of above series as:
1 = (12) – (1-1)
3 = (22) – (2-1)
7 = (32) – (3-1)
13 = (42) – (4-1)
21 = (52) – (5-1)
.
.
.
n-th term = (n2) – (n-1)
Therefore, the n-th term of the actual series will be:
N-th term = 7 * ((n2) - (n-1))
= 7 * (n2 - n + 1)
Below is the implementation of the above approach:
C++
// C++ program to find the N-th term of the series:// 7, 21, 49, 91, 146, 217, 301, 399, ...#include <iostream>#include <math.h>using namespace std;// calculate Nth term of seriesint nthTerm(int n){ return 7 * pow(n, 2) - 7 * n + 7;}// Driver codeint main(){ int N = 4; cout << nthTerm(N); return 0;} |
Java
// Java program to find the N-th term of the series:// 7, 21, 49, 91, 146, 217, 301, 399, ...// calculate Nth term of seriesimport java.util.*;class solution{//Function to find the nth term of the seriesstatic int nthTerm(int n){ return 7 * (int)Math.pow(n, 2) - 7 * n + 7;}// Driver codepublic static void main(String arr[]){ int N = 4; System.out.println(nthTerm(N));}} |
Python3
# Python3 program to find the N-th term of the series:# 7, 21, 49, 91, 146, 217, 301, 399, ...# calculate Nth term of seriesdef nthTerm( n): return 7 * pow(n, 2) - 7 * n + 7# Driver codeN = 4print(nthTerm(N)) |
C#
// C# program to find the // N-th term of the series:// 7, 21, 49, 91, 146, 217, 301, 399, ...using System;// calculate Nth term of seriesclass GFG{// Function to find the Nth // term of the seriesstatic int nthTerm(int n){ return 7 * (int)Math.Pow(n, 2) - 7 * n + 7;}// Driver codepublic static void Main(){ int N = 4; Console.WriteLine(nthTerm(N));}}// This code is contributed // by Akanksha Rai |
PHP
<?php // PHP program to find the// N-th term of the series: // 7, 21, 49, 91, 146, 217, 301, 399, ... function Sum_upto_nth_Term($n) { $r = 7 * pow($n, 2) - 7 * $n + 7; echo $r; } // Driver code $N = 4; Sum_upto_nth_Term($N); // This code is contributed // by Sanjit_Prasad?> |
Javascript
<script>// Javascript program to find the N-th term// of the series:// 7, 21, 49, 91, 146, 217, 301, 399, ...// Calculate Nth term of seriesfunction nthTerm(n){ return 7 * Math.pow(n, 2) - 7 * n + 7;}// Driver codelet N = 4;document.write(nthTerm(N));// This code is contributed by Surbhi Tyagi.</script> |
Output:
91
Time Complexity: O(1)
Auxiliary Space: O(1)
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