Question

Find the first 4 terms of the sequence given by the recursive definition: (see picture for problem)

Answer 1

Answer:

a) 2, 1, 0, -3

Explanations:

The given sequence is:

`\begin{gathered} a_n=na_(n-1)-3 \\ \text{where a}_1=2 \end{gathered}`
`\begin{gathered} \text{Note that:} \\ n\text{ stands for the number of terms} \\ a_n\text{ stands for the nth term} \end{gathered}`

For n = 2

`\begin{gathered} a_2=2a_(2-1)-3 \\ a_2=2a_1-3 \\ a_2=\text{ 2(2)-3} \\ a_2=4-3 \\ a_2=1 \end{gathered}`

For n = 3

`\begin{gathered} a_3=3a_(3-1)-3 \\ a_3=3a_2-3 \\ a_3=3(1)-3 \\ a_3=3-3 \\ a_3=\text{ 0} \end{gathered}`

For n = 4

`\begin{gathered} a_4=4a_(4-1)-3 \\ a_4=\text{ 4(0)-3} \\ a_4=\text{ 0-3} \\ a_4=\text{ -3} \end{gathered}`
`\begin{gathered} a_1=2 \\ a_2=1 \\ a_3=0 \\ a_4=\text{ -3} \end{gathered}`

The first four terms are 2, 1, 0, -3