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Find the sum of an arithmetic progression series, where the user has to enter first number, total number of elements and the common difference.

Arithmetic Progression (A.P.) is a series of numbers in which the difference of any two consecutive numbers is always the same. Here, total number of elements is mentioned as Tn.

Sum of A.P. Series: S_{n}= n/2(2a + (n – 1) d) Tn term of A.P. Series: T_{n}= a + (n – 1) d

Refer an algorithm given below to find the arithmetic progression.

Step 1: Declare variables. Step 2: Initialize sum=0 Step 3: Enter first number of series at runtime. Step 4: Enter total number of series at runtime. Step 5: Enter the common difference at runtime. Step 6: Compute sum by using the formula given below. sum = (num * (2 * a + (num - 1) * diff)) / 2 Step 7: Compute tn by using the formula given below. tn = a + (num - 1) * diff Step 8: For loop i = a; i <= tn; i = i + diff i. if(i != tn) printf("%d + ", i); ii. Else, printf("%d = %d", i, sum); Step 9: Print new line

Following is the C Program to find the sum of arithmetic progression series−

#include <stdio.h> int main() { int a, num, diff, tn, i; int sum = 0; printf(" enter 1st no of series: "); scanf("%d", &a); printf(" enter total no's in series: "); scanf("%d", &num); printf("enter Common Difference: "); scanf("%d", &diff); sum = (num * (2 * a + (num - 1) * diff)) / 2; tn = a + (num - 1) * diff; printf("\n sum of A.P series is : "); for(i = a; i <= tn; i = i + diff){ if(i != tn) printf("%d + ", i); else printf("%d = %d", i, sum); } printf("\n"); return 0; }

When the above program is executed, it produces the following result −

enter 1st no of series: 3 enter total no's in series: 10 enter Common Difference: 5 sum of A.P series is: 3 + 8 + 13 + 18 + 23 + 28 + 33 + 38 + 43 + 48 = 255 enter 1st no of series: 2 enter total no's in series: 15 enter Common Difference: 10 sum of A.P series is: 2 + 12 + 22 + 32 + 42 + 52 + 62 + 72 + 82 + 92 + 102 + 112 + 122 + 132 + 142 = 1080

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