What would be the next number in this series? -3 6 -18 72 -360

Successive multiplication is done using consecutive natural numbers, and then alternating signs.

a_{n}=3\cdot (-1)^{n}\cdot n!=3n!\cdot cos(n{\pi})

Let n=6 to find the next number.

You're welcome.

Yes, I am sure you knew it but did not notice. On my Voyage 200, if I

type in(-1)^{n}, it gives

cos({\pi}n)+i\cdot sin({\pi}n).

Which, as you probably know, is the Euler formula

e^{n\cdot {\pi}\cdot i}

Therefore,(-1)^{n}=e^{n{\pi}i}

It would appear we like this post more than the OP, for they never returned.:rolleyes: