Question

The first term of a geometric sequence is 300 and the common ratio is 0.6. What is the 7th term of the sequence?

Answer 1

$\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=300\\ r=0.6\\ n=7 \end{cases} \\\\\\ a_7=300(0.6)^{7-1}\implies a_7=300(0.6)^6\implies a_7=13.9968$