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C++ program to find n-th term of series 3, 9, 21, 41, 71…
In this problem, we are given an integer N. The task is to find the n-th term in series 3, 9, 21, 41, 71...
Let’s take an example to understand the problem,
Input
N = 7
Output
169
Explanation
The series is 3, 9, 21, 41, 71, 169...
Solution Approach
A simple solution to the problem is by finding the general term of the series. The general term can be found by observing the series a bit. It is,
$$T(N) = \sum n^{2} + \sum n + 1$$
We can directly use the formula for the sum of square of first n natural numbers, first n natural number and then add the three values. At last return the resultant value,
$$T(N)=\left(\frac{n*(n+1)*(2n+1)}{6}\right)+\left(\frac{n*(n+1)}{2}\right)+1$$
Program to illustrate the working of our solution,
Example
#include <iostream>
using namespace std;
int findNthTerm(int n) {
return ((((n)*(n + 1)*(2*n + 1)) / 6) + (n * (n + 1) / 2) + 1);
}
int main() {
int N = 12;
cout<<"The "<<N<<"th term of the series is "<<findNthTerm(N);
return 0;
}Output
The 12th term of the series is 729
Updated on: 13-Mar-2021
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