Challenge: Calculating Sum of Geometric Progression

In the previous chapter, we discovered a formula to calculate the sum of elements of an arithmetic progression. There is also a formula for the sum of a geometric progression:

Let's discover the following real-life case: consider a scenario where a population of bacteria doubles every hour. The initial population is 100 bacteria. We might want to calculate the total population after a certain number of hours. This scenario can be modeled as a geometric progression, where each term represents the population at a specific hour, and the common ratio r is 2 (since the population doubles each hour).

Compito

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Calculate the sum of first n elements of geometric progression using both for loop and the formula described above.

Specify the arguments of the formula.
Specify parameters of for loop.

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Soluzione

def sum_geometric_progression_formula(a, r, n):

sum_formula = a * (1 - r**n) / (1 - r)

return sum_formula

def sum_geometric_progression_loop(a, r, n):

progression_sum = 0

current_term = a

for _ in range(n):

progression_sum += current_term

current_term *= r

return progression_sum

# Example usage

a = 100 # First term

r = 2 # Common ratio

n = 5 # Number of terms in the geometric progression

# Calculate the sum using the formula

sum_formula = sum_geometric_progression_formula(a, r, n)

print(f'Sum using formula is {sum_formula}')

# Calculate the sum using a loop

sum_loop = sum_geometric_progression_loop(a, r, n)

print(f'Sum using loop is {sum_loop}')

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Sezione 1. Capitolo 4

# Function that calculates the sum using formula

def sum_geometric_progression_formula(a, r, n):

sum_formula = a * (1 - r**___) / (1 - ___)