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?

$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 :-

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

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

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation:

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb