Answer:
[tex]a_n=6\cdot (-1)^n[/tex]
Step-by-step explanation:
Alternating Sequences
A sequence whose terms alternate in the sign is called an alternating sequence.
The given sequence consists of the numbers -6 and 6 in infinite alternation.
Such sequences can be expressed as equations of the form
[tex]a_n=a\cdot (-1)^m[/tex]
Where a is the constant absolute value of each term and m is an expression adequately arranged to reproduce the alternation of signs.
Since the sign is minus for odd terms, and plus for even terms, m=n is a good expression for m. Thus:
[tex]a_n=6\cdot (-1)^n[/tex]
