MathGram - for both Mathematics and Programming

Question

Given the first term $a = 5$ and the common difference $d = 3$ , find the sum of the first 50 terms of the arithmetic progression.

Step-by-Step Solution

To solve for the sum of the first $n$ terms of an arithmetic progression, we use the formula:

$S_{n} = \frac{n}{2} \times (2 a + (n - 1) d)$

Where:

$S_{n}$ is the sum of the first $n$ terms
$n$ is the number of terms
$a$ is the first term
$d$ is the common difference

Given:

$a = 5$
$d = 3$
$n = 50$

Substitute these values into the formula:

$S_{50} = \frac{50}{2} \times (2 \times 5 + (50 - 1) \times 3)$

Simplify inside the parentheses:

$S_{50} = 25 \times (10 + 147)$

$S_{50} = 25 \times 157$

Multiply to get the final sum:

$S_{50} = 3925$

So, the sum of the first 50 terms of the arithmetic progression is 3925.

Solving the Problem with Python

Now, let's solve this problem using Python. We will define a function to calculate the sum of the first $n$ terms of an arithmetic progression.

```python
def sum_of_ap(n, a, d):
    # Calculate the sum using the formula
    sum_n = n / 2 * (2 * a + (n - 1) * d)
    return sum_n

# Given values
a = 5
d = 3
n = 50

# Calculate the sum
sum_50_terms = sum_of_ap(n, a, d)
print(f"The sum of the first {n} terms of the arithmetic progression is {sum_50_terms}")

Explanation of the Python Code

Define the Function:
We define a function sum_of_ap that takes the number of terms $n$ , the first term $a$ , and the common difference $d$ as inputs. The function calculates the sum using the arithmetic progression sum formula.
Given Values:
We assign the given values of $a$ , $d$ , and $n$ .
Calculate and Print the Sum:
We call the sum_of_ap function with the given values and print the result.

By following these steps, we've solved a challenging arithmetic progression problem both manually and programmatically. Stay tuned for more math challenges and solutions on SkoolTest!