What is the 10th term of the geometric sequence 2, 1, 1/2?
Answer:
[tex] \tt{Given:} \\ \tt{a_{1} } = 2\\ \tt r = \frac{1}{2} \\ \tt{n}= 10[/tex]
[tex] \tt{a_{n}} = a_{1} {r}^{n - 1} \\ \tt{a_{10}} = 2 {( \frac{1}{2} )}^{10 - 1} \\ \tt{a_{10}} = 2 {( \frac{1}{2} )}^{9} \\ \tt{a_{10}} = 2 ( \frac{1}{512} ) \\ \\ \boxed{ \tt{a_{10}} = \frac{1}{256} }[/tex]
The 10th term is 1/256.
