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# Find the Nth term of the series where each term f[i] = f[i – 1] – f[i – 2] in C++

Suppose we have a series called f. Each term of f, follows this rule f[i] = f[i – 1] – f[i – 2], we have to find the Nth term of this sequence. f[0] = X and f[1] = Y. If X = 2 and Y = 3, and N = 3. The result will be -2.

If we see this closely, there will be almost six terms before the sequence starts repeating itself. So we will find the first 6 terms of the series and then the Nth term will be the same as (N mod 6)th term.

## Example

#include< iostream> using namespace std; int searchNthTerm(int x, int y, int n) { int terms[6]; terms[0] = x; terms[1] = y; for (int i = 2; i < = 5; i++) terms[i] = terms[i - 1] - terms[i - 2]; return terms[n % 6]; } int main() { int x = 2, y = 3, n = 3; cout << "Term at index " < < n << " is: "<< searchNthTerm(x, y, n); }

## Output

Term at index 3 is: -2

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