Question

The 5th term in a geometric sequence is 16 and the 10th term is 1/2. Find the 12th term

Answer 1

`\hspace{13em} \begin{array}{cll} term&value\\ \cline{1-2} a_5&16\\ a_6&16r\\ a_7&16rr\\ a_8&16rrr\\ a_9&16rrrr\\ a_(10)&16rrrrr=(1)/(2)\\ a_(11)&(1)/(2)r\\ a_(12)&(1)/(2)rr \end{array}~\hfill \\\\\\ 16r^5=\cfrac{1}{2}\implies r^5=\cfrac{1}{32}\implies r=\sqrt[5]{\cfrac{1}{32}}\implies r=\cfrac{1}{2} \\\\[-0.35em] ~\dotfill\\\\ a_(12)=\cfrac{1}{2}rr\implies a_(12)=\cfrac{1}{2}r^2\implies a_(12)=\cfrac{1}{2}\left( \cfrac{1}{2} \right)^2\implies a_(12)=\cfrac{1}{8}`