A sweepstakes gives away $1000000, by giving away $25 in

Villaretq0

Villaretq0

Answered question

2022-06-13

A sweepstakes gives away $1000000, by giving away $25 in the first week, $75 in the second week, $225 in the third week, and so on.
How many weeks will it take to give away all the prize money?

Answer & Explanation

scoseBexgofvc

scoseBexgofvc

Beginner2022-06-14Added 20 answers

First week giveaway =25 dollars
Second week giveaway = 75 dollars
Third week giveaway = 225 dollars

S n = 25 + 75 + 255 +
Given: S n = 1000000
a 2 a 1 = a 3 a 2 = 3 1 = γ
S n = a ( γ n 1 ) γ 1
Where γ = 3, a = 25, S n = 1000000
1000000 = 25 ( 3 n 1 ) 3 1
80000 = 3 n 1
80001 = 3 n
ln ( 80001 ) = n ln ( 3 )
n = ln ( 80001 ) ln ( 3 )
n = 10.27641375
n 11   w e e k s

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