Question

Find the twenty-fifth term of an = (-1)".425 =DONE ✔The fourth term of an =(12)" isDONE

Answer 1

Given-

`\begin{gathered} a_n=(-1)^n \\ a_n=((1)/(2))^n \end{gathered}`

=Required- To find out the following,

`a_(25)\text{ and }_{\text{ }}a_4`

Explanation- For finding the value of

`a_(25),`

Putting n=25 in our given sequence we get,

`a_(25)=(-1)^(25)`

Since, odd power to a negative number gives a negative result. Hence,

`a_(25)=-1`

For the second part,

`\begin{gathered} a_n=((1)/(2))^n \\ a_4=((1)/(2))^4 \end{gathered}`

which on further solving gives,

`\begin{gathered} a_4=((1)^4)/((2)^4) \\ =(1)/(16) \end{gathered}`

Final Answer-

`\begin{gathered} a_(25)=-1 \\ a_4=(1)/(16) \end{gathered}`