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# C Program for N-th term of Arithmetic Progression series

Given ‘a’ the First term, ‘d’ the common difference and ‘n’ for the number of terms in a series. The task is to find the nth term of the series.

So, before discussing how to write a program for the problem first we should know what is Arithmetic Progression.

Arithmetic progression or arithmetic sequence is a sequence of number where the difference between the two consecutive terms is same.

Like we have first term i.e a =5, difference 1 and nth term we want to find should be 3. So, the series would be: 5, 6, 7 so the output must be 7.

So, we can say that Arithmetic Progression for nth term will be like −

AP1 = a1 AP2 = a1 + (2-1) * d AP3 = a1 + (3-1) * d ..APn = a1 + (n-1) *

So the formula will be AP = a + (n-1) * d.

## Example

Input: a=2, d=1, n=5 Output: 6 Explanation: The series will be: 2, 3, 4, 5, 6 nth term will be 6 Input: a=7, d=2, n=3 Output: 11

**Approach we will be using to solve the given problem** −

- Take first term A, common difference D, and N the number of series.
- Then calculate nth term by (A + (N - 1) * D)
- Return the Output obtained from the above calculation.

## Algorithm

Start Step 1 -> In function int nth_ap(int a, int d, int n) Return (a + (n - 1) * d) Step 2 -> int main() Declare and initialize the inputs a=2, d=1, n=5 Print The result obtained from calling the function nth_ap(a,d,n) Stop

## Example

#include <stdio.h> int nth_ap(int a, int d, int n) { // using formula to find the // Nth term t(n) = a(1) + (n-1)*d return (a + (n - 1) * d); } //main function int main() { // starting number int a = 2; // Common difference int d = 1; // N th term to be find int n = 5; printf("The %dth term of AP :%d\n", n, nth_ap(a,d,n)); return 0; }

## Output

The 5th term of the series is: 6

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