Question

Determine the 8th term in the geometric sequence whose first term is -10 and whose common ratio is 2

Answer 1

$\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-10\\ r=2\\ n=8 \end{cases} \\\\\\ a_8=-10\cdot 2^{8-1}\implies a_8=-10\cdot 2^7 \\\\\\ a_8=-10\cdot 128\implies a_8=-1280$