Solve Geometric Sequence Word Problem in Gossipopolis

[ThomasMagnus]

I'm having trouble with a word problem:

The people of Gossipopolis cannot keep a secret. Upon being told a secret, a person from Gossipopolis will spend the next hour telling three people. In turn, those friends will spend the next hour each telling 3 more people. This process continues and no one will tell someone who already knows the secret. If you tell a person from Gossipopolis a secret, how many people excluding you, will know the secret after 7 hours?

Here is my attempt:

In the first hour 3 people are told, therefore a=3

Each hour they tell 3 more, therefore common ratio is 3

Over 7 hours, therefore N=7

Find the sum of the first 7 terms formed by the geometric series: 3,9,27...

Sn=a[(R^n)-1]/(R-1)
S7=3[(3^7)-1]/(3-1)
Sum of the seven terms equals 3,279
The person who was originally told the secret also has to be added. Therefore, after seven hours 3,280 people will know the secret.


The answer in the book says 1093. I think this is a mistake because they seemed to work out the equation wrong. Am I doing this correctly?

Thanks!

 

[Manarius]

1093 is the sum of the first six terms, plus one. Looks like the answer in the book is a mistake.

 

[sjb-2812]

1093 is the sum of the first six terms, plus one. Looks like the answer in the book is a mistake.

I don't think so, you are adding 1+3+9+27+81+243+729, not 3+9+27+81+243+729+2187, read the question again (you only tell one person the secret)

 

[Manarius]

I don't think so, you are adding 1+3+9+27+81+243+729, not 3+9+27+81+243+729+2187, read the question again (you only tell one person the secret)

Yes, but it doesn't take you an hour to tell the one person.

You tell 1 person.

He tells 3 people (1 hour gone)

They tell 9 people (2 hours gone)

They tell 27 (3 hours gone)

81 (4 hours)

243 (5 hours)

729 (6 hours)

2187 (7 hours)

It should be: 1+3+9+27+81+243+729+2187