Question

What is the value of the fourth term in a geometric sequence for which a_(1)=10 and r=10

Answer 1

`n^(th)\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^(n-1)\qquad \begin{cases} a_n=n^(th)\ term\\ n=\stackrel{\textit{term position}}{4}\\ a_1=\stackrel{\textit{first term}}{10}\\ r=\stackrel{\textit{common ratio}}{10} \end{cases} \\\\\\ a_4=10\cdot 10^(4-1)\implies a_4=10\cdot 1000\implies a_4=10000`