Find sum of series 1+2+8+26+80+…….+n

we can not define 1+2+8+26+80+………. series in a simple manner to write  program.

But…..

2,8,26,80,242……………..can be define as below

The way to discover the next term is multiply the next number by 2 and then add it on.

i.e. the next number of 2 is 3

so, 3*2=6+2=8

9*2=18+8=26

27*2=54+26=80…….. and so on

            OR

Far more simply multiply the number by 3 and add 2

So,

2 * 3 + 2 = 8;

8 * 3 + 2 = 28

26 *3 + 2 = 80

80 *3 + 2 = 242. and so on

next_term=3*last_term+2

Now for finding the sum of the given series and add 1 with sum of this  series.

C language implementation

 

// C program to add 1+2+8+26+80+…….+n
//Author: Sani Kamal
//Date: 04-Oct-17

#include<stdio.h>

int main(){

int n,temp=0,i,sum=0,hold=0;
 printf("How many term");
 scanf("%d",&n);
 for(i=0;i<n-1;i++){
 temp =3*hold+2;
 hold=temp;
 sum +=hold;
 }
 printf("sum=%d\n",sum+1);
}

Java language implementation

import java.util.Scanner;

/**
 * Java program to add 1+2+8+26+80+.......+n
 *
 * @author Sani Kamal
 */
public class SeriesSum {

public static void main(String[] args) {
 Scanner input = new Scanner(System.in);
 System.out.print("How many term?");
 int n = input.nextInt();
 int temp, hold = 0, sum = 0;
 for (int i = 0; i < n - 1; i++) {
 temp = 3 * hold + 2;
 hold = temp;
 sum += hold;

}
 System.out.println("Sum=" + (sum+1));

}

}

 

Python language implementation

# Python program to add 1+2+8+26+80+.......+n
# Author: Sani Kamal
# Date: 04-Oct-17

num = int(input("How many term?"))
hold = 0
sum=0
for i in range(0, num - 1):
    temp = 3 * hold + 2
    hold = temp
    sum += hold
print(sum + 1)