Question

Find the 4th term in the sequencewith the following definition:aj = 0an = 2(an-1-3)

Answer 1

-60

Step-by-step explanation:

To find the 4th term we need to also find the 2nd and 3rd terms as follows:

`\begin{gathered} a_n=2(a_(n-1)-3) \\ a_2=2(a_(2-1)-3) \\ a_2=2(a_1-3) \\ a_2=2(0-3) \\ a_2=2(-3) \\ a_2=-6 \end{gathered}`
`\begin{gathered} a_3=2(a_(_2)-3) \\ a_3=2(-6-3) \\ a_3=3(-9) \\ a_3=-27 \end{gathered}`

Finally, we can calculate the value of the 4th term as:

`\begin{gathered} a_4=2(a_3-3) \\ a_4=2(-27-3) \\ a_4=2(-30) \\ a_4=-60 \end{gathered}`

So, the answer is -60