Question

Write the explicit formula that represents the geometric sequene -2,8,-32,128

Answer 1

Well, is a geometric sequence, the first term's value is -2

to get the subsequent term's value, we'd multiply by "something" so-called the "common ratio"

well, if we simply just divide any of those values by the one before it, the quotient must be the "common ratio".

hmm say for exampl -32/8 = -4  <---- there's our common ratio

$\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-2\\ r=-4 \end{cases}\implies a_n=-2 (-4)^{n-1}$