Question

1,1,2,6,24,_,_,_,_A) explain and complete the sequenceB) write an explicit and recursive formula for the sequence

Answer 1

As you can notice, this sequence is detailed as follows:

`\begin{gathered} 1\cdot1=1 \\ 1\cdot2=2 \\ 2\cdot3=6 \\ 6\cdot4=24 \end{gathered}`

Now, let's find the next four terms:

`\begin{gathered} 24\cdot5=120 \\ 120\cdot6=720 \\ 720\cdot7=5040 \\ 5040\cdot8=40320 \end{gathered}`

A possible formula could be:

`a_n=n\cdot a_(n-1)`

Where "n" is the number of the term given and it starts from 1. (a0 is 1) This is:

`\begin{gathered} a_1=1.a_(1-1)=1\cdot a_0=1_{} \\ a_2=2\cdot a_(2-1)=2\cdot a_1=2 \\ a_3=3\cdot a_(3-1)=3\cdot a_2=6 \\ \text{and so on } \end{gathered}`