Question

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

Answer 1

well, since we know is a geometric sequence, we can always get the common ratio of it by simply dividing one value by the one behind it... so let's do so, with say hmm -32 and 8 -32/8 = -4 <-- our common ratio

the first term is -2


`\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)`