## Calculus: Early Transcendentals (2nd Edition)

a) $-6$ and $7$ b) $a_{n+1} = |a_n + 1| * (-1)^n$, $a_1 = 1$ c) $a_n = (-1)^{n+1} n$
a) The absolute value of the number is increasing, with the terms alternating in signs. Thus, the next two terms would be $-6$ and $7$ b) Since the first term is 1, $a_1 = 1$. The absolute value increases by one every iteration and it alternates signs, starting with positive. $a_{n+1} = |a_n + 1| * (-1)^n$ c) The $n$ reflects the absolute value, and the sign is even whenever the $n$ is odd. Thus, the formula would be: $a_n = (-1)^{n+1} n$