Question

What is the third term of the recursive sequence below

Answer 1

Given the sequence:

`\begin{gathered} a_1=-6 \\ a_n=(1)/(2)a_(n-1)-n \end{gathered}`

Let's find the third term of the sequence.

To find the third term, a3, we have:

First find the second term, a2:

`\begin{gathered} a_2=(1)/(2)a_(2-1)-2 \\ \\ a_2=(1)/(2)a_1-2 \\ \\ a_2=(1)/(2)(-6)-2 \\ \\ a_2=-3-2 \\ \\ a_2=-5 \end{gathered}`

The second term is -5.

To find the third term, we have:

`\begin{gathered} a_3=(1)/(2)a_(3-1)-3 \\ \\ a_3=(1)/(2)a_2-3 \\ \\ a_3=(1)/(2)(-5)-3 \\ \\ a_3=-2.5-3 \\ \\ a_3=-5.5 \end{gathered}`

Therefore, the third term of the