Question

00 pts

The given pattern continues. Write down the nth term of the sequence suggested by the pattern.
-6, 6, -6, 6, -6, 6, ...
Type the nth term of the sequence.
an

Answer 1

`a_n=6\cdot (-1)^n`

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

`a_n=a\cdot (-1)^m`

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:

`a_n=6\cdot (-1)^n`