Brennan has been playing a game where he can create towns and help his empire expand. Each town he has allows him to create 1.15 times as many villagers as he had in the one before. The game gave Brennan 5 villagers to start with. Explain to Brennan how to create an equation to predict the number of villagers in any specific town. Then show how to use your equation to solve for the number of villagers he can create to live in the 15th town

Question

Mercury · Answer

this is basically a geometric sequence where the initial value a1 = 5 and the common ratio is 1.15. (the sequence starts at 5 villagers, then gets multiplied by 1.15 for each new town.)

the explicit formula for a geometric sequence is

$$a_{n} = a_{1}r^{n-1}$$

plug in your a1 and r values. n represents the # of towns, so for town 15 simply plug in n = 15 and evaluate an.

loveu88 · Answer

thank you