The first five terms of the sequence are 6, 24, 120, 720, 5040.
Sequence
A sequence is a series of numbers that follow a specific pattern or function.
A sequence can be finite or infinite.
Given to us
[tex]a_n=\dfrac{(n+3)!}{(n+3)}[/tex]
where n is the [tex]\bold{n^{th}}[/tex] term.
First-term, n=1,
[tex]a_1=\dfrac{(1+3)!}{(1+3)}=\dfrac{4!}{4} = 6[/tex]
Second-term, n=2,
[tex]a_2=\dfrac{(2+3)!}{(2+3)}=\dfrac{5!}{5} = 24[/tex]
Third-term, n=3,
[tex]a_3=\dfrac{(3+3)!}{(3+3)}=\dfrac{6!}{6} = 120[/tex]
Fourth-term, n=4,
[tex]a_4=\dfrac{(4+3)!}{(4+3)}=\dfrac{7!}{7} = 720[/tex]
Fifth-term, n=5,
[tex]a_5=\dfrac{(5+3)!}{(5+3)}=\dfrac{8!}{8} = 5040[/tex]
Hence, the first five terms of the sequence are 6, 24, 120, 720, 5040.
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