Question

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

Answer 1

So hmm the first term is -2

and if we divide one term by the term before it, we'd get the "common ratio" "r"

so hmm say -32/8 that gives us -4, so r = -4

thus $\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1r^{n-1}\qquad \begin{cases} a_1=\textit{first term}\\ r=\textit{common ratio}\\ ----------\\ a_1=-2\\ r=-4 \end{cases}\implies a_n=-2(-4)^{n-1}$