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Geometric Progression Savings Problem: Calculate Total Pennies Saved After 10 Days
Published on May 6, 2026
Word-Problem
This word problem involves calculating the total amount saved in a savings account over 10 days where the deposit doubles each day, starting with 1 penny. The solution uses the formula for the sum of a geometric progression.
Question
Answer
The problem describes a scenario where Vivian starts a savings account and doubles the amount deposited each day.
Day 1: 1 penny
Day 2: 2 pennies
Day 3: 4 pennies
Day 4: 8 pennies
and so on.
Day 1: 1 penny
Day 2: 2 pennies
Day 3: 4 pennies
Day 4: 8 pennies
and so on.
This is a geometric progression where the first term
We need to find the total amount of money saved after 10 days. This means we need to find the sum of the first 10 terms of this geometric progression.
We need to find the total amount of money saved after 10 days. This means we need to find the sum of the first 10 terms of this geometric progression.
The formula for the sum of the first
In this case,
Substituting these values into the formula:
Substituting these values into the formula:
Now, we need to calculate
So, the total number of pennies saved after 10 days is:
The question asks for the amount of money saved. Since the amounts are in pennies, we should convert this total to dollars.
There are 100 pennies in 1 dollar.
So, to convert pennies to dollars, we divide by 100.
Amount in dollars =
Amount in dollars =
There are 100 pennies in 1 dollar.
So, to convert pennies to dollars, we divide by 100.
Amount in dollars =
Amount in dollars =
The final answer is