Answer:
The value of 15th price is $ 3,000,
The total amount of the price is $ 105,000
Step-by-step explanation:
Given,
The First prize is $10,000,
And, each successive prize is $500 less than the preceding prize,
Thus, the prizes are,
10000, 9500, 9000, ......
Which is an AP,
Having first term, a = 10000,
common difference, d = -500,
Number of terms, n = 15,
Thus, the value of the 15th prize = last term of the above sequence
= a + (n -1)d
= 10000 + (15-1)× -500
= 10000 - 7000
= $ 3,000
Also, the total amount of the price = total sum of the above sequence,
[tex]=\frac{n}{2}(2a + (n-1)d)[/tex]
[tex]=\frac{15}{2}(2(10000) + (15-1)\times -500)[/tex]
[tex]=\frac{15}{2}(20000 - 7000)[/tex]
[tex]=\frac{15}{2}(14000)[/tex]
[tex]=15\times 7000[/tex]
= $ 105,000
