Question

write down the first 5 terms of the following recursively defined sequence: asub1= -2; asubn+1= -2asubn plus 4

Answer 1

-2, 8, -12, 28 and -52.

Explanation:

Given the recursively defined sequence:

`\begin{gathered} a_1=-2 \\ a_(n+1)=-2a_n+4 \end{gathered}`

We want to find the first five terms of the sequence.

The second term:

`\begin{gathered} a_2=a_(1+1)=-2a_1+4 \\ \text{ Substitute }a_1=-2 \\ a_2=-2(-2)+4=4+4 \\ \implies a_2=8 \end{gathered}`

The third term:

`\begin{gathered} a_3=a_(2+1)=-2a_2+4 \\ \text{ Substitute }a_2=8 \\ a_3=-2(8)+4=-16+4 \\ \implies a_3=-12 \end{gathered}`

The fourth term:

`\begin{gathered} a_4=a_(3+1)=-2a_3+4 \\ \text{ Substitute }a_3=-12 \\ a_4=-2(-12)+4=24+4 \\ \implies a_4=28 \end{gathered}`

Finally, we find the fifth term:

`\begin{gathered} a_5=a_(4+1)=-2a_4+4 \\ \text{ Substitute }a_4=28 \\ a_5=-2(28)+4=-56+4 \\ \implies a_5=-52 \end{gathered}`

The first five terms of the sequence are -2, 8, -12, 28 and -52.