Question

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

Answer 1

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

Step-by-step explanation:
`\begin{gathered} \text{nth term of the sequemce:} \\ a_n\text{ = }\frac{n!}{n\text{ + 1}} \end{gathered}`

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

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

`\begin{gathered} \text{when n = 2} \\ a_2\text{ = }\frac{2!}{2\text{+1}}\text{ = }(2*1)/(3) \\ a_2\text{ = }(2)/(3) \end{gathered}`
`\begin{gathered} a_3\text{ = }\frac{3!}{3\text{+1}}\text{ = }(3*2*1)/(4) \\ a_3\text{ = }(6)/(4) \\ a_3\text{ = }(3)/(2) \end{gathered}`
`\begin{gathered} a_4\text{ = }\frac{4!}{4\text{+1}}\text{ = }(4*3*2*1)/(5) \\ a_4\text{ = }(24)/(5) \end{gathered}`
`\begin{gathered} a_5\text{ = }\frac{5!}{5\text{+1}}\text{ = }(5*4*3*2*1)/(6) \\ a_5\text{ = }(120)/(6) \\ a_5\text{ = 20} \end{gathered}`

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