Arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. In Python, we can generate an arithmetic progression without storing all the values using different approaches. Let’s explore three different solutions to this problem.

## Solution 1: Using a Generator Function

A generator function allows us to create a sequence of values on-the-fly without storing them in memory. We can define a generator function that generates the arithmetic progression by yielding each term one at a time.

```
def arithmetic_progression(start, diff):
current = start
while True:
yield current
current += diff
# Example usage
progression = arithmetic_progression(2, 3)
for _ in range(5):
print(next(progression))
```

In this solution, we define a generator function called `arithmetic_progression`

that takes the starting term and the difference as parameters. Inside the function, we use an infinite loop to generate each term by yielding it. We then increment the current term by the difference to get the next term.

To use the generator function, we create an instance of it with the desired starting term and difference. We can then iterate over the generator using a `for`

loop and call `next()`

to get each term.

## Solution 2: Using a List Comprehension

If we want to generate a finite arithmetic progression, we can use a list comprehension to create a list of the desired terms. Although this approach stores all the values in memory, it provides a concise way to generate the progression.

```
start = 2
diff = 3
num_terms = 5
progression = [start + i * diff for i in range(num_terms)]
print(progression)
```

In this solution, we define the starting term, difference, and the number of terms we want in the progression. We then use a list comprehension to generate the progression by adding the product of the difference and the index to the starting term for each index in the range of the number of terms.

## Solution 3: Using a Generator Expression

Similar to the list comprehension approach, we can use a generator expression to generate a finite arithmetic progression without storing all the values in memory. The difference is that a generator expression returns an iterator instead of a list.

```
start = 2
diff = 3
num_terms = 5
progression = (start + i * diff for i in range(num_terms))
for term in progression:
print(term)
```

In this solution, we define the starting term, difference, and the number of terms as before. We then use a generator expression enclosed in parentheses to generate the progression. We can iterate over the generator expression using a `for`

loop to access each term.

After exploring these three solutions, the best option depends on the specific requirements of your program. If you need to generate an infinite arithmetic progression or want to conserve memory by not storing all the values, Solution 1 using a generator function is the most suitable. However, if you need a finite progression and prefer a concise syntax, Solution 2 using a list comprehension is a good choice. Solution 3 using a generator expression provides a balance between memory usage and simplicity.

Choose the solution that best fits your needs and enjoy generating arithmetic progressions in Python without storing all the values!

## One Response

Is there any way to do this more easily?