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What is the third term of the recursive sequence below

What is the third term of the recursive sequence below-example-1

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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

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