Given-
[tex]\begin{gathered} a_n=(-1)^n \\ a_n=(\frac{1}{2})^n \end{gathered}[/tex]
=Required- To find out the following,
[tex]a_{25}\text{ and }_{\text{ }}a_4[/tex]
Explanation- For finding the value of
[tex]a_{25},[/tex]
Putting n=25 in our given sequence we get,
[tex]a_{25}=(-1)^{25}[/tex]
Since, odd power to a negative number gives a negative result. Hence,
[tex]a_{25}=-1[/tex]
For the second part,
[tex]\begin{gathered} a_n=(\frac{1}{2})^n \\ a_4=(\frac{1}{2})^4 \end{gathered}[/tex]
which on further solving gives,
[tex]\begin{gathered} a_4=\frac{(1)^4}{(2)^4} \\ =\frac{1}{16} \end{gathered}[/tex]
Final Answer-
[tex]\begin{gathered} a_{25}=-1 \\ a_4=\frac{1}{16} \end{gathered}[/tex]
