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!

[tex]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[/tex]

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shivishivangi1679 shivishivangi1679 · Answer 2 · 2022-06-10T11:02:14+02:00

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

How can sequence be defined?

When all the terms of a geometric sequence are added, then that expression is called geometric series.

Let the formula be

[tex]a_n = (n - 1)! - 1\\\\ a_1 = (1 - 1)! - 1\\ = 0\\\\ a_2 = (2 - 1)! - 1\\ = 0\\\\ a_3 = (3 - 1)! - 1\\ = 1\\\\ a_4 = (4 - 1)! - 1\\= 5\\\\ a_5 = (5 - 1)! - 1\\= 23[/tex]

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

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