Question

what is the explicit formula for a sequence for which the first five terms are 0, 0, 1, 5, and 23? an = (n – 1)! – 1 an = (n – 1)! an = n! – 1 an = n!

Answer 1

$a_1=0;\ a_2=0;\ a_3=1;\ a_4=5;\ a_5=23\\\\Answer:\\\\a_n=(n-1)!-1\\becouse\\a_1=(1-1)!-1=0!-1=1-1=0\\a_2=(2-1)!-1=1!-1=1-1=0\\a_3=(3-1)!-1=2!-1=1\cdot2-1=2-1=1\\a_4=(4-1)!-1=3!-1=1\cdot2\cdot3-1=6-1=5\\a_5=(5-1)!-1=4!-1=1\cdot2\cdot3\cdot4-1=24-1=23$