What are the next two numbers in this sequence: #-2, 6, -24, 120, -720, 5040, ...#?

1 Answer
Mar 22, 2018

Next two numbers in the sequence are

#color(brown)(a_8 = -40320, a_9 = 362880#

Explanation:

#a_1 = -2, a_2 = 6 , a_3 = -24, a_4 = 120, a_5 = -720, a_6 = 5040#

To find #a_7, a_8#

#a_2 / a_1 = 6 / -2 = -3#

#a_3/a_2 = 24/6 = -4#

#a_4 / a_3 = 120/-24 = -5#

#a_6/ a_5 = -720 / 120 = -6#

#a_7 / a_6 = 5040 / 720 = -7#

#:. a_8 = a_7 * (-8) = 5040 * (-8) = -40320#

Similarly, #a_9 = a_8 * -9 =( -40320) * (-9 )= 362880#