Question

The general term of a sequence is given and involves a factorial. Write the first four terms of each sequence:an = 2(n+1)!

Answer 1

We need to write the first four terms of the sequence:

`a_n=2(n+1)!`

The factorial of a number n is defined as:

`n!=n(n-1)(n-2)(n-3)...(1)`

For example:

`5!=5\cdot4\cdot3\cdot2\cdot1`

Thus, we have:

`\begin{gathered} a_1=2(1+1)!=2\cdot2!=2\cdot(2\cdot1)=4 \\ \\ a_2=2(2+1)!=2\cdot3!=2\cdot(3\cdot2\cdot1)=2\cdot6=12 \\ \\ a_3=2(3+1)!=2\cdot4!=2\cdot(4\cdot3\cdot2\cdot1)=2\cdot24=48 \\ \\ a_4=2(4+1)!=2\cdot5!=2\cdot(5\cdot4\cdot3\cdot2\cdot1)=2\cdot120=240 \end{gathered}`

Answer:

The first four terms are: 4, 12, 48, 240