must answered in sequences/series formulas
If the profit earned by a company is $100 in the first year, and doubles each year such that the profit earned in the second year is $200, $400 in the third year and so on. Find the total profit earned by the company in 15 years of operation.
i have figured out on my calculator what the answer is but the answer wont work when i use a formula.. HELP
WIth first term of 100, common factor of 2 and number of years n = 15,
S = 100(2^15 - 1)/(2 - 1) =
or (100+200+400+800+16oo+3200+6400+12800+25600+51200+102400+204800+409800+819200+1638400)100 =
1500
To find the total profit earned by the company in 15 years, we can use the formula for the sum of a geometric series.
In this case, the first term (a₁) of the series is $100, and the common ratio (r) is 2, since the profit is doubling each year.
The formula for the sum of a geometric series is:
Sn = a₁ * (1 - rⁿ) / (1 - r)
Where:
- Sn is the sum of the series
- a₁ is the first term
- r is the common ratio
- n is the number of terms
Plugging in the given values, we can solve for Sn:
Sn = $100 * (1 - 2¹⁵) / (1 - 2)
Calculating this expression will give us the total profit earned by the company in 15 years.