---
title: "Series 1×10+3×20+6×30+…"
subject: "Computer Programming"
chapter: 5
key: "semester_1/computer_programming:series-1x10-3x20"
source: https://www.bctengineer.com/q/semester_1/computer_programming/series-1x10-3x20
site: BCT Engineering
---

# Series 1×10+3×20+6×30+…

Computer Programming · Chapter 5: Control statements

- Asked in: 2071 Chaitra, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/computer_programming/series-1x10-3x20
- Whole chapter: https://www.bctengineer.com/md/semester_1/computer_programming/chapter-5

## Question

Write a program to calculate the series: 1×10+3×20+6×30+…….+ [N(N+1)/2]×10N, where N is an integer term read from the keyboard.

## Short answer

Each term is (i(i+1)/2) * (10i). Sum over i=1 to N using a loop. For N=3, the sum is 250.

## Answer

The `i`-th term is `[i(i+1)/2] × (10 × i)`: the first factor is the triangular number (1, 3, 6, ...) and the second is 10, 20, 30, ... The program adds these terms for `i = 1` to `N`.

```c
#include <stdio.h>
int main(void)
{
    int n, i;
    long sum = 0;
    printf("Enter N: ");
    scanf("%d", &n);
    for (i = 1; i <= n; i++)
        sum += (long)(i * (i + 1) / 2) * (10 * i);   /* term i */
    printf("Sum of the series = %ld\n", sum);
    return 0;
}
```
Output for N = 3:
```text
Enter N: Sum of the series = 250
```

Check: 1×10 + 3×20 + 6×30 = 10 + 60 + 180 = 250.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is the i-th term of the series?
   A. i x 10
   B. [i(i+1)] x 10
   C. [i(i+1)/2] x (10 x i)
   D. i^2 x 10
   Answer: C. Triangular number times 10i. (Key point: Term pattern)

2. What does the program do for each i?
   A. Multiplies all terms
   B. Resets sum each time
   C. Reads a new N
   D. Adds the i-th term to sum from i=1 to N
   Answer: D. sum += term inside a for loop. (Key point: Loop)

3. What is the sum for N = 3?
   A. 250
   B. 210
   C. 180
   D. 60
   Answer: A. 10 + 60 + 180 = 250. (Key point: Check N=3)

4. Which numbers form the first factors 1, 3, 6?
   A. Squares
   B. Triangular numbers
   C. Fibonacci
   D. Primes
   Answer: B. i(i+1)/2 gives 1, 3, 6. (Key point: Triangular factor)

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