GEOMETRIC SERIES PLEASE HELP!!! Chase has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.13 times as many villagers. The game gave Chase 4 villagers to start with. Help Chase expand his empire by solving for how many villagers he can create with 17 towns. Then explain to Chase how to create an equation to predict the number of villagers for any number of towns. Show your work and use complete sentences.

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anonymous · Answer

@phi

phi · Answer

We can find the nth term using http://hotmath.com/hotmath_help/topics/nth-term-of-a-geometric-sequence.html $$ a_n= a_1 r^{n-1} $$ in your problem $a_1=4$ and r= 1.13 We probably don't need that formula. They ask for how many villagers he can create with 17 towns that means the total of all the villagers in all the towns we can use https://en.wikipedia.org/wiki/Geometric_series#Formula $$ S_n= a_1 \frac{1-r^n}{1-r} $$ use n=17, $a_1=4$, r=1.13 you will need a calculator