math 20-1

Question

In a lottery, the first ticket drawn wins a prize of $25. Each ticket after that receives a prize that is twice the value of the preceding prize. if the lottery gives away a total of 20 prize, show how to use a formula to calculate the total amount of the prizes.

Answer 1

Value of the first prize is  $ 25

The ratio of the two consecutive prize values is constant (2). So series is geometric series .

Find the total amount of the 20 prizes by using the formula

S_n = a(1-rⁿ)/(1-r)

Here , a = $25, r = 2, and n = 20.

S₂₀ = 25(1-2⁽²⁰⁾)/(1-2)

    =26214375

So total amount of the 20 prizes is $26214375