Question

Find the next two terms in the sequence. Write a formula for the nth term. Identify the formula as explicit or recursive.-6, 6, -6, 6, -6, 6, …

Answer 1

$-6,6,-6,6,-6,6$

This is an alternating sequence, from the pattern, we can conclude the 7th term is:

$a_7=-6$

The 8th term is:

$a_8=6$

And the formula would be given by:

$\begin{gathered} a_n=6(-1)^n \\ n\in\N \\ n\ge1 \end{gathered}$