Question

A city fundraiser raffle is raffling off 15 cash prizes. First prize is $10,000. Each successive prize is $500 less than the preceding prize. What is the value of the 15th prize? What is the total amount of cash given out by this raffle? The value of the 15th prize is $ The total amount of cash given out by this raffle is $

Answer 1

The value of 15th price is $ 3,000,

The total amount of the price is $ 105,000

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,

`=(n)/(2)(2a + (n-1)d)`

`=(15)/(2)(2(10000) + (15-1)* -500)`

`=(15)/(2)(20000 - 7000)`

`=(15)/(2)(14000)`

`=15* 7000`

= $ 105,000