Question

What is the sum of the described series? Use . A radio station is holding a trivia contest. The prize money starts at $20 for the first question. Each question is tougher than the one before it, and the station doubles the prize money from the previous amount. If the radio station has 8 trivia questions, how much total money will it hand out in prizes?

Answer 1

Answer: $5100

Step-by-step explanation:

Given, The prize money starts at $20 for the first question.

Let a= 20,

Also, Each question is tougher than the one before it, and the station doubles the prize money from the previous amount.

i.e. the sequence prize willbe : $20 , 2 x ($20) , 2² x ($20)x ....

That is its is an geometric progression with the common ratio r= 2,

Since the sum of n terms in GP is given by :-

$S_n=\dfrac{a(r^n-1)}{r-1}, \text{ when }r>1$

So the total money will it hand out in prizes after 8 questions would be :

$S_8=\dfrac{20(2^8-1)}{2-1}=20\times255=5100$

Hence, the total money it will hand out in prizes = $5100