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Write the first five terms of the sequence with an nth term of an=n!/n+1

Write The First Five Terms Of The Sequence With An Nth Term Of Annn1 class=

Sagot :

1/2, 2/3, 3/2, 24/5, 20 (option B)

Explanation:[tex]\begin{gathered} \text{nth term of the sequemce:} \\ a_n\text{ = }\frac{n!}{n\text{ + 1}} \end{gathered}[/tex]

To get the first 5 terms, we will let n = 1, 2, ,3 ,4, 5

[tex]\begin{gathered} when\text{ n = 1 (1st term)} \\ a_1\text{ = }\frac{1!}{1\text{ + 1}}\text{ = }\frac{1}{2} \\ a_1\text{ = }\frac{1}{2} \end{gathered}[/tex]

[tex]\begin{gathered} \text{when n = 2} \\ a_2\text{ = }\frac{2!}{2\text{+1}}\text{ = }\frac{2\times1}{3} \\ a_2\text{ = }\frac{2}{3} \end{gathered}[/tex][tex]\begin{gathered} a_3\text{ = }\frac{3!}{3\text{+1}}\text{ = }\frac{3\times2\times1}{4} \\ a_3\text{ = }\frac{6}{4} \\ a_3\text{ = }\frac{3}{2} \end{gathered}[/tex][tex]\begin{gathered} a_4\text{ = }\frac{4!}{4\text{+1}}\text{ = }\frac{4\times3\times2\times1}{5} \\ a_4\text{ = }\frac{24}{5} \end{gathered}[/tex][tex]\begin{gathered} a_5\text{ = }\frac{5!}{5\text{+1}}\text{ = }\frac{5\times4\times3\times2\times1}{6} \\ a_5\text{ = }\frac{120}{6} \\ a_5\text{ = 20} \end{gathered}[/tex]

The first five terms are 1/2, 2/3, 3/2, 24/5, 20 (option B)

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