Question

Hey! I need some help with the equation for this question. I think it is a_n = a_1 (r) ^ n-1. Please advise.

Answer 1

Here is the question:
Brian has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.17 times as many villagers. The game gave Brian 8 villagers to start with. Help Brian expand his empire by solving for how many villagers he can create with 16 towns. Then explain to Brian how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.

Answer 2

since no one has responded, I'm gonna give it a wack. My first question is can you define a_1 and r?

Answer 3

I think I have the correct formula now.

Crank out the sum of the populations of the 16 towns.

a1 = 8
r = 1.17
n = 16

Post what you get, okay? @Gold1962

Answer 4

Your book should state above the formulas which is which. Look at your text and see which formula is doing what. There are several ways to write the same expression.

Answer 5

Each of your formulas begin with a_n which is the nth term.

We're looking for a sum in the first part of the problem.

Answer 6

Geometric Sequence Formula is a generic term.

Look for the summation or partial sums formula.

We are not looking for a specific term but for the SUM of the first 16 terms.

Answer 7

Ok, I will try to find it. Thanks for your help!

Answer 8

There is nothing wrong with this summation formula I'm using. Let's finish and then you can figure out what's what in your text later.

I ran this through Wolframalpha.com [8*(1 - 1.17^16)] / (1 - 1.17) =

533.2 people in the 16 villages.

Answer 9

You can count the villagers in each town by hand 15 more times and then add all that together.

Answer 10

Ok so that is the answer. Thanks for telling me the equation. I will see if my teacher accepts it haha :)

Answer 11

Thanks again!!

Answer 12

For the second part,

a = 8

n is whichever village of which you want the population.