Answer:
2, -1, -5/2
Step-by-step explanation:
The recursive formula is: [tex]$ a_{n} = \frac{a_{n - 1}}{4} - 2 $[/tex]
Given: [tex]$ a_1 = 2 $[/tex]
Using the recursive formula, we can find the next terms.
[tex]$ a_2 = \frac{a_1}{4} - 2 $[/tex]
[tex]$ = \frac{2}{2} - 2 $[/tex]
[tex]$ = 1 - 2 = -1 $[/tex]
∴ [tex]$ a_2 = -1 $[/tex]
Now, [tex]$ a_3 = \frac{a_2}{4} - 2 $[/tex]
[tex]$ = \frac{-1}{2} - 2 $[/tex]
[tex]$ = \frac{-1 - 4}{2} $[/tex]
[tex]$ \frac{-5}{2} $[/tex]
∴[tex]$ a_3= \frac{-5}{2} $[/tex]
Therefore, the first three terms are: 2, -1, 5/2.
