Question

Describe a pattern in the sequence of numbers. Predict the next number.

1) 1, 2, 6, 24, ___
2) 0, 3, 8, 15, 24, ___

Answer 1

`1)\\1=1*1\\2=1*2\\6=2*3\\24=6*4\\24*5=120\\120*6=720\\\vdots`


`or\\1=1!\\2=2!=1*2\\6=3!=1*2*3\\24=4!=1*2*3*4\\5!=1*2*3*4*5=120\\6!=1*2*3*4*5*6=720\\\vdots\\n!`



`2)\\0=1^2-1=1-1\\3=2^2-1=4-1\\8=3^2-1=9-1\\15=4^2-1=16-1\\24=5^2-1=25-1\\6^2-1=36-1=35\\7^2-1=49-1=48\\\vdots\\n^2-1`