Tickets are drawn to determine first prize money is s100, 000. Each succeeding prize paid 60% as much as the ticket before it. What was the prize money for the 6th ticket drawn? Use the appropriate formula.
The formula you're going to use for this is as follows:
Initial Prize Money x (1 + Fraction of increase)^(ticket number - 1)
=> I'll represent 60% as 0.6
=> So, the answer is 100,000 x (1.60)^6, which you can solve.
I'm sorry, I misread the question as '60% more than the one before it.'
The answer above is incorrect, I'll update the answer
Instead of
100,000 x (1.60)^6
It'll be
100,000 x (0.60)^6
1st prize = 100,000
2nd prize = (.6)(10,000) = 6,000
3rd prize = (.6)^2 (10000) = 3600
...
6th prize = (.6)^5 (10,000) = .....
Ah, misread the question and then accidentally put a 6 in place of a 5
Thanks for the correction
To find the prize money for the 6th ticket drawn, we can use the formula for a geometric sequence. The formula is:
\[ a_n = a_1 \times r^{(n-1)} \]
Where:
- \( a_n \) is the nth term in the sequence (prize money for the nth ticket drawn)
- \( a_1 \) is the first term in the sequence (prize money for the first ticket drawn)
- \( r \) is the common ratio between the terms (60% or 0.60 in this case)
- \( n \) is the position of the term we want to find (in this case, 6th ticket drawn)
Step 1: Identify the given information.
- The first prize money is $100,000 (a_1).
- Each succeeding prize is 60% as much as the ticket before it (common ratio, r = 0.60).
- We want to find the prize money for the 6th ticket drawn (n = 6).
Step 2: Apply the formula.
\[ a_6 = a_1 \times r^{(6-1)} \]
Step 3: Substitute the given values into the formula.
\[ a_6 = 100,000 \times (0.60)^5 \]
Step 4: Solve the equation.
\[ a_6 = 100,000 \times 0.07776 \]
Step 5: Calculate the result.
\[ a_6 = 7,776 \]
Therefore, the prize money for the 6th ticket drawn is $7,776.