A hardware store makes a profit of $41,000 during its first year. The store owner sets a goal of increasing profits by $9000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.
To find the total profit during the first 5 years of business, we need to calculate the sum of the profits for each year.
Given that the hardware store makes a profit of $41,000 during its first year, we can start by adding this profit to our running total:
Year 1 profit: $41,000
Next, we need to add the additional profits for the next 4 years. The store owner sets a goal of increasing profits by $9000 each year for 4 years. To calculate the profits for these years, we can use a simple arithmetic sequence.
The formula for finding the nth term of an arithmetic sequence is:
an = a1 + (n - 1)d
where:
an = nth term of the sequence
a1 = first term of the sequence
n = number of terms
d = common difference between terms
In this case, the first term (a1) is $41,000, and the common difference (d) is $9000. We can now calculate the profits for years 2, 3, 4, and 5:
Year 2 profit: $41,000 + (2 - 1) * $9000 = $50,000
Year 3 profit: $41,000 + (3 - 1) * $9000 = $59,000
Year 4 profit: $41,000 + (4 - 1) * $9000 = $68,000
Year 5 profit: $41,000 + (5 - 1) * $9000 = $77,000
Finally, we can calculate the total profit by summing up all the yearly profits:
Total profit = Year 1 profit + Year 2 profit + Year 3 profit + Year 4 profit + Year 5 profit
= $41,000 + $50,000 + $59,000 + $68,000 + $77,000
Therefore, the total profit during the first 5 years of business is $295,000.
another sum of arithmetic sequence
a = 41,000
d = 9000
n = 5 (so n-1 = 4)
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