Question

Find the pattern and use it to list the next two terms in the sequence.

3, -6, 18, -72, 360, -2,160,___,___.

Answer 1

Hello,

$u_{1} =3=3*1=3*1!*(-1)^{1-1}\\\\ u_{2} =-6=3*(-2)=3*2!*(-1)^{2-1}\\ u_{3} =18=3*3!*(-1)^{3-1}\\ u_{4} =-72=3*4!*(-1)^{4-1}\\ u_{5} =360=3*5!*(-1)^{5-1}\\ u_{6} =-2160=3*6!*(-1)^{6-1}\\ u_{7} =15120=3*7!*(-1)^{7-1}\\ u_{8} =-120960=3*8!*(-1)^{8-1}\\\\ \boxed{ u_{n} =3*n!*(-1)^{n-1}}$