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, nth_ap(a,d,n));
   return 0;
}

Output

The 5th term of the series is: 6