Question

Geometric Sequences?

Answer 1

You have a geometric progression with \[a = 5\] and \[r = 1.15\]. The sum of the first n terms of this progression is \[s_n = 5\left(\frac{1-(1.15)^n}{1-1.15}\right)\]he answer to the first part of the question is \[(s_15 = 5\left( \frac{1-(1.15)^{15}}{1-1.15}\right)) =(47.58) = 47\] villagers. To find the answer to the second part, you know that there are \[s_n\] villagers. To find the number of towns you have to assume hat the maximum number of villagers has been created and rearrange \[ s_n = 5\left( \frac{1-(1.15)^n}{1-1.15}\right)\] to make \[n\] the subject, a follows:
\[5(1−(1.15)^n)=(1−1.15)S_n=−0.15S_n\]
\[5−5(1−(1.15)^n)=−0.15S_n\]
\[5(1.15)^n=5+0.15S_n\]
\[(1.15)^n=\frac{ 5+0.15S_n }{ 5 }\]
\[S_n=\log _{1.155}\frac{ 0.15x }{ 5 }\]

Answer 2

he dedass closed the question -__-

Answer 3

I'm sorry!! Thank you so much though ;v; @Rizags

Answer 4

yea np loooool