# Solution Review: Sequences and Loops

Learn to print different sequences using loops.

## Printing number sequences using loops

In this lesson, we’ll go through the solutions of the problems in the previous lesson.

### Multiples of 10

Our code should print the following sequence:

```
10 20 30 40 50 60
```

#### Solution

Let’s take a look at the solution.

/*This program should print the above number sequence*/#include<iostream>using namespace std;int main(){int limit = 6;for(int i = 1; i <= limit; i++){cout << i * 10 << " ";}return 0;}

The number sequence above is simple. We use the `for`

loop to print the sequence till the appropriate number.

In the editor above, in **line 11**, we initialize the `i`

variable to `1`

. The condition `i <= limit`

, in the same line, executes the body of the loop as long as `i`

is less than or equal to the `limit`

(`6`

, in this case) entered by the user. We display the first six multiples of `10`

by multiplying `10`

with `i`

which is initially `1`

and is incremented by `1`

after each iteration till it is less than or equal to `6`

. The incremental step `i++`

increments `i`

by `1`

after each iteration.

### Odd sequence

Our code should print the following sequence:

```
1 3 5 7 9 11
```

#### Solution

Let’s take a look at the solution.

#include<iostream>using namespace std;int main(){int limit = 11;for(int i = 1; i <= limit; i+=2){cout << i << " ";}return 0;}

The above number sequence is also pretty straightforward. We get the next number by incrementing it by 2, that is, we’ll use `i+=2`

.

### Arithmetic sequence

Our code should print the following sequence:

```
1 1 3 6 5 11 7 16
```

#### Solution

Let’s take a look at the solution.

#include<iostream>using namespace std;int main(){int first = 1;int second = 1;for(int i = 1; i <= 4; i++){// printing the first and second numberscout << first << " ";cout << second << " ";// incrementing the first by 2 and second by 5first = first + 2;second = second + 5;}return 0;}

In the number sequence above, we can see two different patterns. There is a number sequence of odd numbers 1, 3, 5, 7,… with the difference of 2 and then another sequence of 1, 6, 11, 16,… with the difference of 5.

So, to solve this exercise, we declare and initialize two variables `first`

and `second`

as the first two numbers of the sequence. Inside the body of the loop, we display the `first`

and `second`

variables (**lines 12** and **13**) and then increment the `first`

number by `2`

in **line 15** and increment the `second`

number by `5`

in **line 16**.