Answer:
[tex]\begin{cases}a_1 = 2\\\\a_{n} = -4*a_{n-1}\end{cases}[/tex]
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Explanation:
The first line of the answer says "the first term is 2".
The second line says "take any term and multiply by -4 to get the next term".
The [tex]a_n[/tex] represents the nth term while [tex]a_{n-1}[/tex] is the term just before it.
The second line shown above is the same as writing [tex]a_{n+1} = -4*a_n[/tex]
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The -4 is found by dividing any term over its previous one
-8/2 = -4
32/(-8) = -4
-128/32 = -4
512/(-128) = -4
This shows the common ratio is -4 and this sequence is geometric.
